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TILTING COMPLEXES AND CODIMENSION FUNCTIONS OVER COMMUTATIVE NOETHERIAN RINGS Nagoya Math. J. (IF 0.8) Pub Date : 2024-03-15 MICHAL HRBEK, TSUTOMU NAKAMURA, JAN ŠŤOVÍČEK
In the derived category of a commutative noetherian ring, we explicitly construct a silting object associated with each sp-filtration of the Zariski spectrum satisfying the “slice” condition. Our new construction is based on local cohomology and it allows us to study when the silting object is tilting. For a ring admitting a dualizing complex, this occurs precisely when the sp-filtration arises from
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NOTE ON THE THREE-DIMENSIONAL LOG CANONICAL ABUNDANCE IN CHARACTERISTIC Nagoya Math. J. (IF 0.8) Pub Date : 2024-02-28 ZHENG XU
In this paper, we prove the nonvanishing and some special cases of the abundance for log canonical threefold pairs over an algebraically closed field k of characteristic $p> 3$ . More precisely, we prove that if $(X,B)$ be a projective log canonical threefold pair over k and $K_{X}+B$ is pseudo-effective, then $\kappa (K_{X}+B)\geq 0$ , and if $K_{X}+B$ is nef and $\kappa (K_{X}+B)\geq 1$ , then $K_{X}+B$
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COUNTING GEOMETRIC BRANCHES VIA THE FROBENIUS MAP AND F-NILPOTENT SINGULARITIES Nagoya Math. J. (IF 0.8) Pub Date : 2024-02-27 HAILONG DAO, KYLE MADDOX, VAIBHAV PANDEY
We give an explicit formula to count the number of geometric branches of a curve in positive characteristic using the theory of tight closure. This formula readily shows that the property of having a single geometric branch characterizes F-nilpotent curves. Further, we show that a reduced, local F-nilpotent ring has a single geometric branch; in particular, it is a domain. Finally, we study inequalities
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A CALCULATION OF THE PERFECTOIDIZATION OF SEMIPERFECTOID RINGS Nagoya Math. J. (IF 0.8) Pub Date : 2024-02-23 RYO ISHIZUKA
We show that perfectoidization can be (almost) calculated by using p-root closure in certain cases, including the semiperfectoid case. To do this, we focus on the universality of perfectoidizations and uniform completions, as well as the p-root closed property of integral perfectoid rings. Through this calculation, we establish a connection between a classical closure operation “p-root closure” used
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A HOMOMORPHISM BETWEEN BOTT–SAMELSON BIMODULES Nagoya Math. J. (IF 0.8) Pub Date : 2024-01-25 NORIYUKI ABE
In the previous paper, we defined a new category which categorifies the Hecke algebra. This is a generalization of the theory of Soergel bimodules. To prove theorems, the existences of certain homomorphisms between Bott–Samelson bimodules are assumed. In this paper, we prove this assumption. We only assume the vanishing of certain two-colored quantum binomial coefficients.
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TOPICS SURROUNDING THE COMBINATORIAL ANABELIAN GEOMETRY OF HYPERBOLIC CURVES IV: DISCRETENESS AND SECTIONS Nagoya Math. J. (IF 0.8) Pub Date : 2024-01-18 YUICHIRO HOSHI, SHINICHI MOCHIZUKI
Let $\Sigma $ be a nonempty subset of the set of prime numbers which is either equal to the entire set of prime numbers or of cardinality one. In the present paper, we continue our study of the pro- $\Sigma $ fundamental groups of hyperbolic curves and their associated configuration spaces over algebraically closed fields in which the primes of $\Sigma $ are invertible. The present paper focuses on
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DILOGARITHM IDENTITIES IN CLUSTER SCATTERING DIAGRAMS Nagoya Math. J. (IF 0.8) Pub Date : 2023-12-21 TOMOKI NAKANISHI
We extend the notion of y-variables (coefficients) in cluster algebras to cluster scattering diagrams (CSDs). Accordingly, we extend the dilogarithm identity associated with a period in a cluster pattern to the one associated with a loop in a CSD. We show that these identities are constructed from and reduced to trivial ones by applying the pentagon identity possibly infinitely many times.
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LOCAL SECTIONS OF ARITHMETIC FUNDAMENTAL GROUPS OF p-ADIC CURVES Nagoya Math. J. (IF 0.8) Pub Date : 2023-12-20 MOHAMED SAÏDI
We investigate sections of the arithmetic fundamental group $\pi _1(X)$ where X is either a smooth affinoid p-adic curve, or a formal germ of a p-adic curve, and prove that they can be lifted (unconditionally) to sections of cuspidally abelian Galois groups. As a consequence, if X admits a compactification Y, and the exact sequence of $\pi _1(X)$ splits, then $\text {index} (Y)=1$ . We also exhibit
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COEFFICIENT QUIVERS, -REPRESENTATIONS, AND EULER CHARACTERISTICS OF QUIVER GRASSMANNIANS Nagoya Math. J. (IF 0.8) Pub Date : 2023-12-13 JAIUNG JUN, ALEXANDER SISTKO
A quiver representation assigns a vector space to each vertex, and a linear map to each arrow of a quiver. When one considers the category $\mathrm {Vect}(\mathbb {F}_1)$ of vector spaces “over $\mathbb {F}_1$ ” (the field with one element), one obtains $\mathbb {F}_1$ -representations of a quiver. In this paper, we study representations of a quiver over the field with one element in connection to
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-ZARISKI PAIRS OF SURFACE SINGULARITIES Nagoya Math. J. (IF 0.8) Pub Date : 2023-12-05 CHRISTOPHE EYRAL, MUTSUO OKA
Let $f_0$ and $f_1$ be two homogeneous polynomials of degree d in three complex variables $z_1,z_2,z_3$ . We show that the Lê–Yomdin surface singularities defined by $g_0:=f_0+z_i^{d+m}$ and $g_1:=f_1+z_i^{d+m}$ have the same abstract topology, the same monodromy zeta-function, the same $\mu ^*$ -invariant, but lie in distinct path-connected components of the $\mu ^*$ -constant stratum if their projective
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HOW TO EXTEND CLOSURE AND INTERIOR OPERATIONS TO MORE MODULES Nagoya Math. J. (IF 0.8) Pub Date : 2023-12-01 NEIL EPSTEIN, REBECCA R. G., JANET VASSILEV
There are several ways to convert a closure or interior operation to a different operation that has particular desirable properties. In this paper, we axiomatize three ways to do so, drawing on disparate examples from the literature, including tight closure, basically full closure, and various versions of integral closure. In doing so, we explore several such desirable properties, including hereditary
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ON A COMPARISON BETWEEN DWORK AND RIGID COHOMOLOGIES OF PROJECTIVE COMPLEMENTS Nagoya Math. J. (IF 0.8) Pub Date : 2023-12-01 JUNYEONG PARK
For homogeneous polynomials $G_1,\ldots ,G_k$ over a finite field, their Dwork complex is defined by Adolphson and Sperber, based on Dwork’s theory. In this article, we will construct an explicit cochain map from the Dwork complex of $G_1,\ldots ,G_k$ to the Monsky–Washnitzer complex associated with some affine bundle over the complement $\mathbb {P}^n\setminus X_G$ of the common zero $X_G$ of $G_1
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GENUS CURVES WITH BAD REDUCTION AT ONE ODD PRIME Nagoya Math. J. (IF 0.8) Pub Date : 2023-11-29 ANDRZEJ DĄBROWSKI, MOHAMMAD SADEK
The problem of classifying elliptic curves over $\mathbb Q$ with a given discriminant has received much attention. The analogous problem for genus $2$ curves has only been tackled when the absolute discriminant is a power of $2$ . In this article, we classify genus $2$ curves C defined over ${\mathbb Q}$ with at least two rational Weierstrass points and whose absolute discriminant is an odd prime.
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NON-ISOMORPHIC SMOOTH COMPACTIFICATIONS OF THE MODULI SPACE OF CUBIC SURFACES Nagoya Math. J. (IF 0.8) Pub Date : 2023-10-03 SEBASTIAN CASALAINA-MARTIN, SAMUEL GRUSHEVSKY, KLAUS HULEK, RADU LAZA
The well-studied moduli space of complex cubic surfaces has three different, but isomorphic, compact realizations: as a GIT quotient ${\mathcal {M}}^{\operatorname {GIT}}$ , as a Baily–Borel compactification of a ball quotient ${(\mathcal {B}_4/\Gamma )^*}$ , and as a compactified K-moduli space. From all three perspectives, there is a unique boundary point corresponding to non-stable surfaces. From
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EXACT SUBCATEGORIES, SUBFUNCTORS OF , AND SOME APPLICATIONS Nagoya Math. J. (IF 0.8) Pub Date : 2023-09-27 HAILONG DAO, SOUVIK DEY, MONALISA DUTTA
Let $({\cal{A}},{\cal{E}})$ be an exact category. We establish basic results that allow one to identify sub(bi)functors of ${\operatorname{Ext}}_{\cal{E}}(-,-)$ using additivity of numerical functions and restriction to subcategories. We also study a small number of these new functors over commutative local rings in detail and find a range of applications from detecting regularity to understanding
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A BALL QUOTIENT PARAMETRIZING TRIGONAL GENUS 4 CURVES Nagoya Math. J. (IF 0.8) Pub Date : 2023-09-21 EDUARD LOOIJENGA
We consider the moduli space of genus 4 curves endowed with a $g^1_3$ (which maps with degree 2 onto the moduli space of genus 4 curves). We prove that it defines a degree $\frac {1}{2}(3^{10}-1)$ cover of the nine-dimensional Deligne–Mostow ball quotient such that the natural divisors that live on that moduli space become totally geodesic (their normalizations are eight-dimensional ball quotients)
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NEW MODULI SPACES OF ONE-DIMENSIONAL SHEAVES ON Nagoya Math. J. (IF 0.8) Pub Date : 2023-09-18 DAPENG MU
We define a one-dimensional family of Bridgeland stability conditions on $\mathbb {P}^n$ , named “Euler” stability condition. We conjecture that the “Euler” stability condition converges to Gieseker stability for coherent sheaves. Here, we focus on ${\mathbb P}^3$ , first identifying Euler stability conditions with double-tilt stability conditions, and then we consider moduli of one-dimensional sheaves
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EXTENSIONS OF CHARACTERS IN TYPE D AND THE INDUCTIVE MCKAY CONDITION, I Nagoya Math. J. (IF 0.8) Pub Date : 2023-09-08 BRITTA SPÄTH
This is a contribution to the study of $\mathrm {Irr}(G)$ as an $\mathrm {Aut}(G)$-set for G a finite quasisimple group. Focusing on the last open case of groups of Lie type $\mathrm {D}$ and $^2\mathrm {D}$, a crucial property is the so-called $A'(\infty )$ condition expressing that diagonal automorphisms and graph-field automorphisms of G have transversal orbits in $\mathrm {Irr}(G)$. This is part
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ON THE DISTRIBUTION OF IWASAWA INVARIANTS ASSOCIATED TO MULTIGRAPHS Nagoya Math. J. (IF 0.8) Pub Date : 2023-09-08 CÉDRIC DION, ANTONIO LEI, ANWESH RAY, DANIEL VALLIÈRES
Let $\ell $ be a prime number. The Iwasawa theory of multigraphs is the systematic study of growth patterns in the number of spanning trees in abelian $\ell $-towers of multigraphs. In this context, growth patterns are realized by certain analogs of Iwasawa invariants, which depend on the prime $\ell $ and the abelian $\ell $-tower of multigraphs. We formulate and study statistical questions about
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SUPPORT THEOREM FOR PINNED DIFFUSION PROCESSES Nagoya Math. J. (IF 0.8) Pub Date : 2023-09-08 YUZURU INAHAMA
In this paper, we prove a support theorem of Stroock–Varadhan type for pinned diffusion processes. To this end, we use two powerful results from stochastic analysis. One is quasi-sure analysis for Brownian rough path. The other is Aida–Kusuoka–Stroock’s positivity theorem for the densities of weighted laws of non-degenerate Wiener functionals.
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MULTIPLIERS AND CHARACTERIZATION OF THE DUAL OF NEVANLINNA-TYPE SPACES Nagoya Math. J. (IF 0.8) Pub Date : 2023-09-07 MIECZYSŁAW MASTYŁO, BARTOSZ STANIÓW
The Nevanlinna-type spaces $N_\varphi $ of analytic functions on the disk in the complex plane generated by strongly convex functions $\varphi $ in the sense of Rudin are studied. We show for some special class of strongly convex functions asymptotic bounds on the growth of the Taylor coefficients of a function in $N_\varphi $ and use these to characterize the coefficient multipliers from $N_\varphi
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TILINGS OF THE SPHERE BY CONGRUENT QUADRILATERALS II: EDGE COMBINATION WITH RATIONAL ANGLES Nagoya Math. J. (IF 0.8) Pub Date : 2023-09-07 YIXI LIAO, ERXIAO WANG
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of $a^3b$-quadrilaterals with all angles being rational degrees. There are $12$ sporadic and $3$ infinite sequences of quadrilaterals admitting the two-layer earth map tilings together
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A VARIANT OF PERFECTOID ABHYANKAR’S LEMMA AND ALMOST COHEN–MACAULAY ALGEBRAS Nagoya Math. J. (IF 0.8) Pub Date : 2023-09-04 KEI NAKAZATO, KAZUMA SHIMOMOTO
In this article, we prove that a complete Noetherian local domain of mixed characteristic $p>0$ with perfect residue field has an integral extension that is an integrally closed, almost Cohen–Macaulay domain such that the Frobenius map is surjective modulo p. This result is seen as a mixed characteristic analog of the fact that the perfect closure of a complete local domain in positive characteristic
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ON THE ESSENTIAL TORSION FINITENESS OF ABELIAN VARIETIES OVER TORSION FIELDS Nagoya Math. J. (IF 0.8) Pub Date : 2023-08-24 JEFFREY D. ACHTER, LIAN DUAN, XIYUAN WANG
The classical Mordell–Weil theorem implies that an abelian variety A over a number field K has only finitely many K-rational torsion points. This finitude of torsion still holds even over the cyclotomic extension $K^{\mathrm {cyc}}=K{\mathbb Q}^{\mathrm {ab}}$ by a result of Ribet. In this article, we consider the finiteness of torsion points of an abelian variety A over the infinite algebraic extension
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ON THE ANTI-CANONICAL GEOMETRY OF WEAK -FANO THREEFOLDS, III Nagoya Math. J. (IF 0.8) Pub Date : 2023-08-22 CHEN JIANG, YU ZOU
For a terminal weak ${\mathbb {Q}}$-Fano threefold X, we show that the mth anti-canonical map defined by $|-mK_X|$ is birational for all $m\geq 59$.
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-PERPENDICULAR WIDE SUBCATEGORIES Nagoya Math. J. (IF 0.8) Pub Date : 2023-08-22 ASLAK BAKKE BUAN, ERIC J. HANSON
Let $\Lambda $ be a finite-dimensional algebra. A wide subcategory of $\mathsf {mod}\Lambda $ is called left finite if the smallest torsion class containing it is functorially finite. In this article, we prove that the wide subcategories of $\mathsf {mod}\Lambda $ arising from $\tau $-tilting reduction are precisely the Serre subcategories of left-finite wide subcategories. As a consequence, we show
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ERRATUM TO “NON-UNIFORMLY FLAT AFFINE ALGEBRAIC HYPERSURFACES” Nagoya Math. J. (IF 0.8) Pub Date : 2023-06-06 ARINDAM MANDAL, VAMSI PRITHAM PINGALI, DROR VAROLIN
In this erratum, we correct an erroneous result in [PV2] and prove that the affine algebraic hypersurfaces $xy^2=1$ and $z=xy^2$ are not interpolating with respect to the Gaussian weight.
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ON A BERNSTEIN–SATO POLYNOMIAL OF A MEROMORPHIC FUNCTION Nagoya Math. J. (IF 0.8) Pub Date : 2023-06-06 KIYOSHI TAKEUCHI
We define Bernstein–Sato polynomials for meromorphic functions and study their basic properties. In particular, we prove a Kashiwara–Malgrange-type theorem on their geometric monodromies, which would also be useful in relation with the monodromy conjecture. A new feature in the meromorphic setting is that we have several b-functions whose roots yield the same set of the eigenvalues of the Milnor monodromies
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CONCAVITY PROPERTY OF MINIMAL INTEGRALS WITH LEBESGUE MEASURABLE GAIN Nagoya Math. J. (IF 0.8) Pub Date : 2023-06-05 QI’AN GUAN, ZHENG YUAN
In this article, we present a concavity property of the minimal $L^{2}$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain. As applications, we give necessary conditions for our concavity degenerating to linearity, characterizations for 1-dimensional case, and a characterization for the holding of the equality in optimal $L^2$ extension problem on open Riemann surfaces with
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TWISTED SHIFT-INVARIANT SYSTEM IN Nagoya Math. J. (IF 0.8) Pub Date : 2023-06-05 SANTI RANJAN DAS, RABEETHA VELSAMY, RADHA RAMAKRISHNAN
We consider a general twisted shift-invariant system, $V^{t}(\mathcal {A})$, consisting of twisted translates of countably many generators and study the problem of obtaining a characterization for the system $V^{t}(\mathcal {A})$ to form a frame sequence or a Riesz sequence. We illustrate our theory with some examples. In addition to these results, we study a dual twisted shift-invariant system and
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K-STABLE DIVISORS IN Nagoya Math. J. (IF 0.8) Pub Date : 2023-04-28 IVAN CHELTSOV, KENTO FUJITA, TAKASHI KISHIMOTO, TAKUZO OKADA
We prove that every smooth divisor in $\mathbb {P}^1\times \mathbb {P}^1\times \mathbb {P}^2$ of degree $(1,1,2)$ is K-stable.
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KRONECKER LIMIT FUNCTIONS AND AN EXTENSION OF THE ROHRLICH–JENSEN FORMULA Nagoya Math. J. (IF 0.8) Pub Date : 2023-04-11 JAMES W. COGDELL, JAY JORGENSON, LEJLA SMAJLOVIĆ
In [20], Rohrlich proved a modular analog of Jensen’s formula. Under certain conditions, the Rohrlich–Jensen formula expresses an integral of the log-norm $\log \Vert f \Vert $ of a ${\mathrm {PSL}}(2,{\mathbb {Z}})$ modular form f in terms of the Dedekind Delta function evaluated at the divisor of f. In [2], the authors re-interpreted the Rohrlich–Jensen formula as evaluating a regularized inner product
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LINES ON HOLOMORPHIC CONTACT MANIFOLDS AND A GENERALIZATION OF -DISTRIBUTIONS TO HIGHER DIMENSIONS Nagoya Math. J. (IF 0.8) Pub Date : 2023-02-23 JUN-MUK HWANG, QIFENG LI
Since the celebrated work by Cartan, distributions with small growth vector $(2,3,5)$ have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic $(2,3,5)$-distributions and nondegenerate lines on holomorphic contact manifolds of dimension 5. We generalize this correspondence to higher dimensions by studying nondegenerate lines on holomorphic contact
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A CATEGORIFICATION OF ACYCLIC PRINCIPAL COEFFICIENT CLUSTER ALGEBRAS Nagoya Math. J. (IF 0.8) Pub Date : 2023-02-22 MATTHEW PRESSLAND
In earlier work, the author introduced a method for constructing a Frobenius categorification of a cluster algebra with frozen variables by starting from the data of an internally Calabi–Yau algebra, which becomes the endomorphism algebra of a cluster-tilting object in the resulting category. In this paper, we construct appropriate internally Calabi–Yau algebras for cluster algebras with polarized
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K-THEORY OF NON-ARCHIMEDEAN RINGS II Nagoya Math. J. (IF 0.8) Pub Date : 2023-02-21 MORITZ KERZ, SHUJI SAITO, GEORG TAMME
We study fundamental properties of analytic K-theory of Tate rings such as homotopy invariance, Bass fundamental theorem, Milnor excision, and descent for admissible coverings.
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CONSTRUCTING MAXIMAL COFINITARY GROUPS Nagoya Math. J. (IF 0.8) Pub Date : 2023-01-30 DAVID SCHRITTESSER
Improving and clarifying a construction of Horowitz and Shelah, we show how to construct (in $\mathsf {ZF}$, i.e., without using the Axiom of Choice) maximal cofinitary groups. Among the groups we construct, one is definable by a formula in second-order arithmetic with only a few natural number quantifiers.
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ON AN AVERAGE GOLDBACH REPRESENTATION FORMULA OF FUJII Nagoya Math. J. (IF 0.8) Pub Date : 2023-01-17 DANIEL A. GOLDSTON, ADE IRMA SURIAJAYA
Fujii obtained a formula for the average number of Goldbach representations with lower-order terms expressed as a sum over the zeros of the Riemann zeta function and a smaller error term. This assumed the Riemann Hypothesis. We obtain an unconditional version of this result and obtain applications conditional on various conjectures on zeros of the Riemann zeta function.
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ANNIHILATORS AND DIMENSIONS OF THE SINGULARITY CATEGORY Nagoya Math. J. (IF 0.8) Pub Date : 2023-01-06 JIAN LIU
Let R be a commutative Noetherian ring. We prove that if R is either an equidimensional finitely generated algebra over a perfect field, or an equidimensional equicharacteristic complete local ring with a perfect residue field, then the annihilator of the singularity category of R coincides with the Jacobian ideal of R up to radical. We establish a relationship between the annihilator of the singularity
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GENERIC LINES IN PROJECTIVE SPACE AND THE KOSZUL PROPERTY Nagoya Math. J. (IF 0.8) Pub Date : 2023-01-06 JOSHUA ANDREW RICE
In this paper, we study the Koszul property of the homogeneous coordinate ring of a generic collection of lines in $\mathbb {P}^n$ and the homogeneous coordinate ring of a collection of lines in general linear position in $\mathbb {P}^n.$ We show that if $\mathcal {M}$ is a collection of m lines in general linear position in $\mathbb {P}^n$ with $2m \leq n+1$ and R is the coordinate ring of $\mathcal
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NORMAL AND IRREDUCIBLE ADIC SPACES, THE OPENNESS OF FINITE MORPHISMS, AND A STEIN FACTORIZATION Nagoya Math. J. (IF 0.8) Pub Date : 2022-12-16 LUCAS MANN
We transfer several elementary geometric properties of rigid-analytic spaces to the world of adic spaces, more precisely to the category of adic spaces which are locally of (weakly) finite type over a non-archimedean field. This includes normality, irreducibility (in particular, irreducible components), and a Stein factorization theorem. Most notably, we show that a finite morphism in our category
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ENRIQUES INVOLUTIONS AND BRAUER CLASSES Nagoya Math. J. (IF 0.8) Pub Date : 2022-12-13 A. N. SKOROBOGATOV, D. VALLONI
We prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In generic cases, this gives a bijection between the set ${\mathcal Enr}(X)$ of Enriques quotients of X up to isomorphism and the set of Brauer classes of X of order 2. For some K3 surfaces of Picard rank $20,$ we prove that the fibers of ${\mathcal Enr}(X)\to \mathrm {{Br}}(X)[2]$
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EXACT SOLUTIONS FOR THE SINGULARLY PERTURBED RICCATI EQUATION AND EXACT WKB ANALYSIS Nagoya Math. J. (IF 0.8) Pub Date : 2022-12-08 NIKITA NIKOLAEV
The singularly perturbed Riccati equation is the first-order nonlinear ordinary differential equation $\hbar \partial _x f = af^2 + bf + c$ in the complex domain where $\hbar $ is a small complex parameter. We prove an existence and uniqueness theorem for exact solutions with prescribed asymptotics as $\hbar \to 0$ in a half-plane. These exact solutions are constructed using the Borel–Laplace method;
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BIG COHEN–MACAULAY TEST IDEALS IN EQUAL CHARACTERISTIC ZERO VIA ULTRAPRODUCTS Nagoya Math. J. (IF 0.8) Pub Date : 2022-12-07 TATSUKI YAMAGUCHI
Utilizing ultraproducts, Schoutens constructed a big Cohen–Macaulay (BCM) algebra $\mathcal {B}(R)$ over a local domain R essentially of finite type over $\mathbb {C}$. We show that if R is normal and $\Delta $ is an effective $\mathbb {Q}$-Weil divisor on $\operatorname {Spec} R$ such that $K_R+\Delta $ is $\mathbb {Q}$-Cartier, then the BCM test ideal $\tau _{\widehat {\mathcal {B}(R)}}(\widehat
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ON THE MILNOR FIBRATION OF CERTAIN NEWTON DEGENERATE FUNCTIONS Nagoya Math. J. (IF 0.8) Pub Date : 2022-12-01 CHRISTOPHE EYRAL, MUTSUO OKA
It is well known that the diffeomorphism type of the Milnor fibration of a (Newton) nondegenerate polynomial function f is uniquely determined by the Newton boundary of f. In the present paper, we generalize this result to certain degenerate functions, namely we show that the diffeomorphism type of the Milnor fibration of a (possibly degenerate) polynomial function of the form $f=f^1\cdots f^{k_0}$
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SEMIAMPLENESS FOR CALABI–YAU SURFACES IN POSITIVE AND MIXED CHARACTERISTIC Nagoya Math. J. (IF 0.8) Pub Date : 2022-11-28 FABIO BERNASCONI, LIAM STIGANT
In this note, we prove the semiampleness conjecture for Kawamata log terminal Calabi–Yau (CY) surface pairs over an excellent base ring. As applications, we deduce that generalized abundance and Serrano’s conjecture hold for surfaces. Finally, we study the semiampleness conjecture for CY threefolds over a mixed characteristic DVR.
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FROBENIUS-AFFINE STRUCTURES AND TANGO CURVES Nagoya Math. J. (IF 0.8) Pub Date : 2022-11-24 YUICHIRO HOSHI
In a previous paper, we discussed Frobenius-projective structures on projective smooth curves in positive characteristic and established a relationship between pseudo-coordinates and Frobenius-indigenous structures by means of Frobenius-projective structures. In the present paper, we discuss an “affine version” of this study of Frobenius-projective structures. More specifically, we discuss Frobenius-affine
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ANALYTIC SPREAD OF FILTRATIONS ON TWO-DIMENSIONAL NORMAL LOCAL RINGS Nagoya Math. J. (IF 0.8) Pub Date : 2022-11-23 STEVEN DALE CUTKOSKY
In this paper, we prove that a classical theorem by McAdam about the analytic spread of an ideal in a Noetherian local ring continues to be true for divisorial filtrations on a two-dimensional normal excellent local ring R, and that the Hilbert polynomial of the fiber cone of a divisorial filtration on R has a Hilbert function which is the sum of a linear polynomial and a bounded function. We prove
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COHOMOLOGY OF THE BRUHAT–TITS STRATA IN THE UNRAMIFIED UNITARY RAPOPORT–ZINK SPACE OF SIGNATURE Nagoya Math. J. (IF 0.8) Pub Date : 2022-11-23 JOSEPH MULLER
In their renowned paper (2011, Inventiones Mathematicae 184, 591–627), I. Vollaard and T. Wedhorn defined a stratification on the special fiber of the unitary unramified PEL Rapoport–Zink space with signature $(1,n-1)$ . They constructed an isomorphism between the closure of a stratum, called a closed Bruhat–Tits stratum, and a Deligne–Lusztig variety which is not of classical type. In this paper,
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AN OBSERVATION ON THE DIRICHLET PROBLEM AT INFINITY IN RIEMANNIAN CONES Nagoya Math. J. (IF 0.8) Pub Date : 2022-11-22 JEAN C. CORTISSOZ
In this short paper, we show a sufficient condition for the solvability of the Dirichlet problem at infinity in Riemannian cones (as defined below). This condition is related to a celebrated result of Milnor that classifies parabolic surfaces. When applied to smooth Riemannian manifolds with a special type of metrics, which generalize the class of metrics with rotational symmetry, we obtain generalizations
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IWASAWA THEORY FOR p-TORSION CLASS GROUP SCHEMES IN CHARACTERISTIC p Nagoya Math. J. (IF 0.8) Pub Date : 2022-11-22 JEREMY BOOHER, BRYDEN CAIS
We investigate a novel geometric Iwasawa theory for ${\mathbf Z}_p$ -extensions of function fields over a perfect field k of characteristic $p>0$ by replacing the usual study of p-torsion in class groups with the study of p-torsion class group schemes. That is, if $\cdots \to X_2 \to X_1 \to X_0$ is the tower of curves over k associated with a ${\mathbf Z}_p$ -extension of function fields totally ramified
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MINIMAL ( -)TILTING INFINITE ALGEBRAS Nagoya Math. J. (IF 0.8) Pub Date : 2022-10-11 KAVEH MOUSAVAND, CHARLES PAQUETTE
Motivated by a new conjecture on the behavior of bricks, we start a systematic study of minimal $\tau $ -tilting infinite (min- $\tau $ -infinite, for short) algebras. In particular, we treat min- $\tau $ -infinite algebras as a modern counterpart of minimal representation-infinite algebras and show some of the fundamental similarities and differences between these families. We then relate our studies
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TORSORS AND STABLE EQUIVARIANT BIRATIONAL GEOMETRY Nagoya Math. J. (IF 0.8) Pub Date : 2022-10-11 BRENDAN HASSETT, YURI TSCHINKEL
We develop the formalism of universal torsors in equivariant birational geometry and apply it to produce new examples of nonbirational but stably birational actions of finite groups.
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LAURICELLA HYPERGEOMETRIC FUNCTIONS, UNIPOTENT FUNDAMENTAL GROUPS OF THE PUNCTURED RIEMANN SPHERE, AND THEIR MOTIVIC COACTIONS Nagoya Math. J. (IF 0.8) Pub Date : 2022-09-26 FRANCIS BROWN, CLÉMENT DUPONT
The goal of this paper is to raise the possibility that there exists a meaningful theory of ‘motives’ associated with certain hypergeometric integrals, viewed as functions of their parameters. It goes beyond the classical theory of motives, but should be compatible with it. Such a theory would explain a recent and surprising conjecture arising in the context of scattering amplitudes for a motivic Galois
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CORRIGENDUM TO “CLUSTER CATEGORIES FROM GRASSMANNIANS AND ROOT COMBINATORICS” Nagoya Math. J. (IF 0.8) Pub Date : 2022-09-08 KARIN BAUR, DUSKO BOGDANIC, ANA GARCIA ELSENER
In this note, we correct an oversight regarding the modules from Definition 4.2 and proof of Lemma 5.12 in Baur et al. (Nayoga Math. J., 2020, 240, 322–354). In particular, we give a correct construction of an indecomposable rank $2$ module $\operatorname {\mathbb {L}}\nolimits (I,J)$ , with the rank 1 layers I and J tightly $3$ -interlacing, and we give a correct proof of Lemma 5.12.
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ADJUNCTION AND INVERSION OF ADJUNCTION Nagoya Math. J. (IF 0.8) Pub Date : 2022-09-05 OSAMU FUJINO, KENTA HASHIZUME
We establish adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality.
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A BRICK VERSION OF A THEOREM OF AUSLANDER Nagoya Math. J. (IF 0.8) Pub Date : 2022-09-05 FRANCESCO SENTIERI
We prove that a finite-dimensional algebra $ \Lambda $ is $ \tau $ -tilting finite if and only if all the bricks over $ \Lambda $ are finitely generated. This is obtained as a consequence of the existence of proper locally maximal torsion classes for $ \tau $ -tilting infinite algebras.
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EVALUATION OF CERTAIN EXOTIC (1)-SERIES Nagoya Math. J. (IF 0.8) Pub Date : 2022-09-05 MARTA NA CHEN, WENCHANG CHU
A class of exotic $_3F_2(1)$ -series is examined by integral representations, which enables the authors to present relatively easier proofs for a few remarkable formulae. By means of the linearization method, these $_3F_2(1)$ -series are further extended with two integer parameters. A general summation theorem is explicitly established for these extended series, and several sample summation identities
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GENERALIZED ZETA INTEGRALS ON CERTAIN REAL PREHOMOGENEOUS VECTOR SPACES Nagoya Math. J. (IF 0.8) Pub Date : 2022-09-05 WEN-WEI LI
Let X be a real prehomogeneous vector space under a reductive group G, such that X is an absolutely spherical G-variety with affine open orbit. We define local zeta integrals that involve the integration of Schwartz–Bruhat functions on X against generalized matrix coefficients of admissible representations of $G(\mathbb {R})$ , twisted by complex powers of relative invariants. We establish the convergence
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ON -ACTIONS ON K3 SURFACES IN POSITIVE CHARACTERISTIC Nagoya Math. J. (IF 0.8) Pub Date : 2022-09-05 YUYA MATSUMOTO
In characteristic $0$ , symplectic automorphisms of K3 surfaces (i.e., automorphisms preserving the global $2$ -form) and non-symplectic ones behave differently. In this paper, we consider the actions of the group schemes $\mu _{n}$ on K3 surfaces (possibly with rational double point [RDP] singularities) in characteristic p, where n may be divisible by p. We introduce the notion of symplecticness of
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NON-PERVERSE PARITY SHEAVES ON THE FLAG VARIETY Nagoya Math. J. (IF 0.8) Pub Date : 2022-08-23 PETER J. MCNAMARA
We give examples of non-perverse parity sheaves on Schubert varieties for all primes.