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GRADED TWISTED CALABI–YAU ALGEBRAS ARE GENERALIZED ARTIN–SCHELTER REGULAR Nagoya Math. J. (IF 0.556) Pub Date : 2021-02-02 MANUEL L. REYES; DANIEL ROGALSKI
This is a general study of twisted Calabi–Yau algebras that are $\mathbb {N}$-graded and locally finite-dimensional, with the following major results. We prove that a locally finite graded algebra is twisted Calabi–Yau if and only if it is separable modulo its graded radical and satisfies one of several suitable generalizations of the Artin–Schelter regularity property, adapted from the work of Martinez-Villa
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ON ORDINARY ENRIQUES SURFACES IN POSITIVE CHARACTERISTIC Nagoya Math. J. (IF 0.556) Pub Date : 2020-12-22 ROBERTO LAFACE; SOFIA TIRABASSI
We give a notion of ordinary Enriques surfaces and their canonical lifts in any positive characteristic, and we prove Torelli-type results for this class of Enriques surfaces.
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THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS Nagoya Math. J. (IF 0.556) Pub Date : 2020-12-04 MICHELE BOLOGNESI; NÉSTOR FERNÁNDEZ VARGAS
Let C be a hyperelliptic curve of genus $g \geq 3$ . In this paper, we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on C with trivial determinant. In order to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb {P}^1)^{2g}//\text {PGL(2)}$ . Then, we identify the restriction
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ANALYTIC SPREAD AND INTEGRAL CLOSURE OF INTEGRALLY DECOMPOSABLE MODULES Nagoya Math. J. (IF 0.556) Pub Date : 2020-11-03 CARLES BIVIÀ-AUSINA; JONATHAN MONTAÑO
We relate the analytic spread of a module expressed as the direct sum of two submodules with the analytic spread of its components. We also study a class of submodules whose integral closure can be expressed in terms of the integral closure of its row ideals, and therefore can be obtained by means of a simple computer algebra procedure. In particular, we analyze a class of modules, not necessarily
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CLASS NUMBERS OF CM ALGEBRAIC TORI, CM ABELIAN VARIETIES AND COMPONENTS OF UNITARY SHIMURA VARIETIES Nagoya Math. J. (IF 0.556) Pub Date : 2020-10-28 JIA-WEI GUO; NAI-HENG SHEU; CHIA-FU YU
We give a formula for the class number of an arbitrary complex mutliplication (CM) algebraic torus over $\mathbb {Q}$ . This is proved based on results of Ono and Shyr. As applications, we give formulas for numbers of polarized CM abelian varieties, of connected components of unitary Shimura varieties and of certain polarized abelian varieties over finite fields. We also give a second proof of our
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ERRATUM: CONTINUITY OF HILBERT–KUNZ MULTIPLICITY AND F-SIGNATURE Nagoya Math. J. (IF 0.556) Pub Date : 2020-10-23 THOMAS POLSTRA; ILYA SMIRNOV
Unfortunately, there is a mistake in [PS, Lemma 3.10] which invalidates [PS, Theorem 3.12]. We show that the theorem still holds if the ring is assumed to be Gorenstein.
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ON THE OPTIMAL $L^{2}$ EXTENSION THEOREM AND A QUESTION OF OHSAWA Nagoya Math. J. (IF 0.556) Pub Date : 2020-10-23 SHA YAO; ZHI LI; XIANGYU ZHOU
In this paper, we present a version of Guan-Zhou’s optimal $L^{2}$ extension theorem and its application. As a main application, we show that under a natural condition, the question posed by Ohsawa in his series paper VIII on the extension of $L^{2}$ holomorphic functions holds. We also give an explicit counterexample which shows that the question fails in general.
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ON THE SHARPNESS OF TIAN’S CRITERION FOR K-STABILITY Nagoya Math. J. (IF 0.556) Pub Date : 2020-10-23 YUCHEN LIU; ZIQUAN ZHUANG
Tian’s criterion for K-stability states that a Fano variety of dimension n whose alpha invariant is greater than ${n}{/(n+1)}$ is K-stable. We show that this criterion is sharp by constructing n-dimensional singular Fano varieties with alpha invariants ${n}{/(n+1)}$ that are not K-polystable for sufficiently large n. We also construct K-unstable Fano varieties with alpha invariants ${(n-1)}{/n}$ .
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ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS Nagoya Math. J. (IF 0.556) Pub Date : 2020-09-28 S. A. SEYED FAKHARI
Assume that G is a graph with edge ideal $I(G)$ and star packing number $\alpha _2(G)$ . We denote the sth symbolic power of $I(G)$ by $I(G)^{(s)}$ . It is shown that the inequality $ \operatorname {\mathrm {depth}} S/(I(G)^{(s)})\geq \alpha _2(G)-s+1$ is true for every chordal graph G and every integer $s\geq 1$ . Moreover, it is proved that for any graph G, we have $ \operatorname {\mathrm {depth}}
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QUASI-SPLIT SYMMETRIC PAIRS OF $U(\mathfrak {gl}_N)$ AND THEIR SCHUR ALGEBRAS Nagoya Math. J. (IF 0.556) Pub Date : 2020-09-21 YIQIANG LI; JIERU ZHU
We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric counterpart of the above Schur algebras in [1] specialized at $q=1$ .
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ANALYTIC PROPERTIES OF EISENSTEIN SERIES AND STANDARD -FUNCTIONS Nagoya Math. J. (IF 0.556) Pub Date : 2020-07-21 OLIVER STEIN
We prove a functional equation for a vector valued real analytic Eisenstein series transforming with the Weil representation of $\operatorname{Sp}(n,\mathbb{Z})$ on $\mathbb{C}[(L^{\prime }/L)^{n}]$. By relating such an Eisenstein series with a real analytic Jacobi Eisenstein series of degree $n$, a functional equation for such an Eisenstein series is proved. Employing a doubling method for Jacobi
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TOPOLOGIES ON SCHEMES AND MODULUS PAIRS Nagoya Math. J. (IF 0.556) Pub Date : 2020-07-13 BRUNO KAHN; HIROYASU MIYAZAKI
We study relationships between the Nisnevich topology on smooth schemes and certain Grothendieck topologies on proper and not necessarily proper modulus pairs, which were introduced in previous papers. Our results play an important role in the theory of sheaves with transfers on proper modulus pairs.
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GROTHENDIECK GROUPS OF TRIANGULATED CATEGORIES VIA CLUSTER TILTING SUBCATEGORIES Nagoya Math. J. (IF 0.556) Pub Date : 2020-06-11 FRANCESCA FEDELE
Let $k$ be a field, and let ${\mathcal{C}}$ be a $k$-linear, Hom-finite triangulated category with split idempotents. In this paper, we show that under suitable circumstances, the Grothendieck group of ${\mathcal{C}}$, denoted by $K_{0}({\mathcal{C}})$, can be expressed as a quotient of the split Grothendieck group of a higher cluster tilting subcategory of ${\mathcal{C}}$. The results we prove are
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DEGENERATING 0 IN TRIANGULATED CATEGORIES Nagoya Math. J. (IF 0.556) Pub Date : 2020-06-08 MANUEL SAORÍN; ALEXANDER ZIMMERMANN
In previous work, based on the work of Zwara and Yoshino, we defined and studied degenerations of objects in triangulated categories analogous to the degeneration of modules. In triangulated categories ${\mathcal{T}}$, it is surprising that the zero object may degenerate. We show that the triangulated subcategory of ${\mathcal{T}}$ generated by the objects that are degenerations of zero coincides with
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MINIMAL MODEL THEORY FOR LOG SURFACES IN FUJIKI’S CLASS Nagoya Math. J. (IF 0.556) Pub Date : 2020-06-05 OSAMU FUJINO
We establish the minimal model theory for $\mathbb{Q}$-factorial log surfaces and log canonical surfaces in Fujiki’s class ${\mathcal{C}}$.
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MASS GROWTH OF OBJECTS AND CATEGORICAL ENTROPY Nagoya Math. J. (IF 0.556) Pub Date : 2020-06-04 AKISHI IKEDA
In the pioneering work by Dimitrov–Haiden–Katzarkov–Kontsevich, they introduced various categorical analogies from the classical theory of dynamical systems. In particular, they defined the entropy of an endofunctor on a triangulated category with a split generator. In the connection between the categorical theory and the classical theory, a stability condition on a triangulated category plays the
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HIGHER DEFORMATIONS OF LIE ALGEBRA REPRESENTATIONS II Nagoya Math. J. (IF 0.556) Pub Date : 2020-06-02 MATTHEW WESTAWAY
Steinberg’s tensor product theorem shows that for semisimple algebraic groups, the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the preceding paper in this series, deforming the distribution algebra of a higher Frobenius kernel yielded a family of deformations called higher reduced enveloping algebras
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CHARACTERIZING THE MOD- LOCAL LANGLANDS CORRESPONDENCE BY NILPOTENT GAMMA FACTORS Nagoya Math. J. (IF 0.556) Pub Date : 2020-05-12 GILBERT MOSS
Let $F$ be a $p$-adic field and choose $k$ an algebraic closure of $\mathbb{F}_{\ell }$, with $\ell$ different from $p$. We define “nilpotent lifts” of irreducible generic $k$-representations of $GL_{n}(F)$, which take coefficients in Artin local $k$-algebras. We show that an irreducible generic $\ell$-modular representation $\unicode[STIX]{x1D70B}$ of $GL_{n}(F)$ is uniquely determined by its collection
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WEIERSTRASS–KENMOTSU REPRESENTATION OF WILLMORE SURFACES IN SPHERES Nagoya Math. J. (IF 0.556) Pub Date : 2020-04-27 JOSEF F. DORFMEISTER; PENG WANG
A Willmore surface $y:M\rightarrow S^{n+2}$ has a natural harmonic oriented conformal Gauss map $Gr_{y}:M\rightarrow SO^{+}(1,n+3)/SO(1,3)\times SO(n)$, which maps each point $p\in M$ to its oriented mean curvature 2-sphere at $p$. An easy observation shows that all conformal Gauss maps of Willmore surfaces satisfy a restricted nilpotency condition, which will be called “strongly conformally harmonic
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ON THE ASSOCIATED PRIMES OF LOCAL COHOMOLOGY Nagoya Math. J. (IF 0.556) Pub Date : 2018-02-05 HAILONG DAO; PHAM HUNG QUY
Let $R$ be a commutative Noetherian ring of prime characteristic $p$ . In this paper, we give a short proof using filter regular sequences that the set of associated prime ideals of $H_{I}^{t}(R)$ is finite for any ideal $I$ and for any $t\geqslant 0$ when $R$ has finite $F$ -representation type or finite singular locus. This extends a previous result by Takagi–Takahashi and gives affirmative answers
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STRONGLY QUASI-HEREDITARY ALGEBRAS AND REJECTIVE SUBCATEGORIES Nagoya Math. J. (IF 0.556) Pub Date : 2018-02-27 MAYU TSUKAMOTO
Ringel’s right-strongly quasi-hereditary algebras are a distinguished class of quasi-hereditary algebras of Cline–Parshall–Scott. We give characterizations of these algebras in terms of heredity chains and right rejective subcategories. We prove that any artin algebra of global dimension at most two is right-strongly quasi-hereditary. Moreover we show that the Auslander algebra of a representation-finite
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LITTLEWOOD–PALEY CHARACTERIZATIONS OF ANISOTROPIC WEAK MUSIELAK–ORLICZ HARDY SPACES Nagoya Math. J. (IF 0.556) Pub Date : 2018-03-16 BO LI; RUIRUI SUN; MINFENG LIAO; BAODE LI
Let $A$ be an expansive dilation on $\mathbb{R}^{n}$ and $\unicode[STIX]{x1D711}:\mathbb{R}^{n}\times [0,\infty )\rightarrow [0,\infty )$ an anisotropic growth function. In this article, the authors introduce the anisotropic weak Musielak–Orlicz Hardy space $\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$ via the nontangential grand maximal function and then obtain its Littlewood–Paley characterizations
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FRACTIONAL FOCK–SOBOLEV SPACES Nagoya Math. J. (IF 0.556) Pub Date : 2018-03-06 HONG RAE CHO; SOOHYUN PARK
Let $s\in \mathbb{R}$ and $0
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MULTIPLICATION FORMULAS AND SEMISIMPLICITY FOR $q$ -SCHUR SUPERALGEBRAS Nagoya Math. J. (IF 0.556) Pub Date : 2018-04-30 JIE DU; HAIXIA GU; ZHONGGUO ZHOU
We investigate products of certain double cosets for the symmetric group and use the findings to derive some multiplication formulas for the $q$ -Schur superalgebras. This gives a combinatorialization of the relative norm approach developed in Du and Gu (A realization of the quantum supergroup $\mathbf{U}(\mathfrak{g}\mathfrak{l}_{m|n})$ , J. Algebra 404 (2014), 60–99). We then give several applications
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RANKIN–SELBERG CONVOLUTIONS OF NONCUSPIDAL HALF-INTEGRAL WEIGHT MAASS FORMS IN THE PLUS SPACE Nagoya Math. J. (IF 0.556) Pub Date : 2018-05-21 YOSHINORI MIZUNO
The author gives the analytic properties of the Rankin–Selberg convolutions of two half-integral weight Maass forms in the plus space. Applications to the Koecher–Maass series associated with nonholomorphic Siegel–Eisenstein series are given.
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DISTRIBUTION OF GALOIS GROUPS OF MAXIMAL UNRAMIFIED 2-EXTENSIONS OVER IMAGINARY QUADRATIC FIELDS Nagoya Math. J. (IF 0.556) Pub Date : 2018-07-09 SOSUKE SASAKI
Let $k$ be an imaginary quadratic field with $\operatorname{Cl}_{2}(k)\simeq V_{4}$ . It is known that the length of the Hilbert $2$ -class field tower is at least $2$ . Gerth (On 2-class field towers for quadratic number fields with $2$ -class group of type $(2,2)$ , Glasgow Math. J. 40(1) (1998), 63–69) calculated the density of $k$ where the length of the tower is $1$ ; that is, the maximal unramified
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GORENSTEIN HOMOLOGICAL PROPERTIES OF TENSOR RINGS Nagoya Math. J. (IF 0.556) Pub Date : 2018-06-07 XIAO-WU CHEN; MING LU
Let $R$ be a two-sided Noetherian ring, and let $M$ be a nilpotent $R$ -bimodule, which is finitely generated on both sides. We study Gorenstein homological properties of the tensor ring $T_{R}(M)$ . Under certain conditions, the ring $R$ is Gorenstein if and only if so is $T_{R}(M)$ . We characterize Gorenstein projective $T_{R}(M)$ -modules in terms of $R$ -modules.
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GENERATORS, RELATIONS, AND HOMOLOGY FOR OZSVÁTH–SZABÓ’S KAUFFMAN-STATES ALGEBRAS Nagoya Math. J. (IF 0.556) Pub Date : 2020-04-17 ANDREW MANION; MARCO MARENGON; MICHAEL WILLIS
We give a generators-and-relations description of differential graded algebras recently introduced by Ozsváth and Szabó for the computation of knot Floer homology. We also compute the homology of these algebras and determine when they are formal.
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BERNSTEIN–SATO ROOTS FOR MONOMIAL IDEALS IN POSITIVE CHARACTERISTIC Nagoya Math. J. (IF 0.556) Pub Date : 2020-03-20 EAMON QUINLAN-GALLEGO
Following the work of Mustaţă and Bitoun, we recently developed a notion of Bernstein–Sato roots for arbitrary ideals, which is a prime characteristic analogue for the roots of the Bernstein–Sato polynomial. Here, we prove that for monomial ideals the roots of the Bernstein–Sato polynomial (over $\mathbb{C}$) agree with the Bernstein–Sato roots of the mod $p$ reductions of the ideal for $p$ large enough
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COIDEMPOTENT SUBCOALGEBRAS AND SHORT EXACT SEQUENCES OF FINITARY 2-REPRESENTATIONS Nagoya Math. J. (IF 0.556) Pub Date : 2020-03-19 AARON CHAN; VANESSA MIEMIETZ
In this article, we study short exact sequences of finitary 2-representations of a weakly fiat 2-category. We provide a correspondence between such short exact sequences with fixed middle term and coidempotent subcoalgebras of a coalgebra 1-morphism defining this middle term. We additionally relate these to recollements of the underlying abelian 2-representations.
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LOCAL DUALITY FOR THE SINGULARITY CATEGORY OF A FINITE DIMENSIONAL GORENSTEIN ALGEBRA Nagoya Math. J. (IF 0.556) Pub Date : 2020-03-11 DAVE BENSON; SRIKANTH B. IYENGAR; HENNING KRAUSE; JULIA PEVTSOVA
A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the $\mathfrak{p}$-local and $\mathfrak{p}$-torsion subcategories of the derived category, for each homogeneous
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NON-SYMPLECTIC INVOLUTIONS ON MANIFOLDS OF -TYPE Nagoya Math. J. (IF 0.556) Pub Date : 2020-02-27 CHIARA CAMERE; ALBERTO CATTANEO; ANDREA CATTANEO
We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant quadratic forms of the invariant and coinvariant lattice for the action of the involution on cohomology and explicitly describe the lattices in the cases where the invariant lattice has small rank
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A BETTER COMPARISON OF $\operatorname{cdh}$ - AND $l\operatorname{dh}$ -COHOMOLOGIES Nagoya Math. J. (IF 0.556) Pub Date : 2019-09-13 SHANE KELLY
In order to work with non-Nagata rings which are Nagata “up-to-completely-decomposed-universal-homeomorphism,” specifically finite rank Hensel valuation rings, we introduce the notions of pseudo-integral closure, pseudo-normalization, and pseudo-Hensel valuation ring. We use this notion to give a shorter and more direct proof that $H_{\operatorname{cdh}}^{n}(X,F_{\operatorname{cdh}})=H_{l\operatorname{dh}}^{n}(X
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DUALITY OF (2, 3, 5)-DISTRIBUTIONS AND LAGRANGIAN CONE STRUCTURES Nagoya Math. J. (IF 0.556) Pub Date : 2020-01-23 GOO ISHIKAWA; YUMIKO KITAGAWA; ASAHI TSUCHIDA; WATARU YUKUNO
As was shown by a part of the authors, for a given $(2,3,5)$ -distribution $D$ on a five-dimensional manifold $Y$ , there is, locally, a Lagrangian cone structure $C$ on another five-dimensional manifold $X$ which consists of abnormal or singular paths of $(Y,D)$ . We give a characterization of the class of Lagrangian cone structures corresponding to $(2,3,5)$ -distributions. Thus, we complete the
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INVARIANCE OF CERTAIN PLURIGENERA FOR SURFACES IN MIXED CHARACTERISTICS Nagoya Math. J. (IF 0.556) Pub Date : 2020-01-16 ANDREW EGBERT; CHRISTOPHER D. HACON
We prove the deformation invariance of Kodaira dimension and of certain plurigenera and the existence of canonical models for log surfaces which are smooth over an integral Noetherian scheme $S$ .
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AROUND THE NEARBY CYCLE FUNCTOR FOR ARITHMETIC $\mathscr{D}$ -MODULES Nagoya Math. J. (IF 0.556) Pub Date : 2019-08-28 TOMOYUKI ABE
We will establish a nearby and vanishing cycle formalism for the arithmetic $\mathscr{D}$ -module theory following Beilinson’s philosophy. As an application, we define smooth objects in the framework of arithmetic $\mathscr{D}$ -modules whose category is equivalent to the category of overconvergent isocrystals.
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A FUNCTIONAL LOGARITHMIC FORMULA FOR THE HYPERGEOMETRIC FUNCTION $_{3}F_{2}$ Nagoya Math. J. (IF 0.556) Pub Date : 2018-09-14 MASANORI ASAKURA; NORIYUKI OTSUBO
We give a sufficient condition for the hypergeometric function $_{3}F_{2}$ to be a linear combination of the logarithm of algebraic functions.
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AN ALGEBRO-GEOMETRIC STUDY OF SPECIAL VALUES OF HYPERGEOMETRIC FUNCTIONS $_{3}F_{2}$ Nagoya Math. J. (IF 0.556) Pub Date : 2018-09-13 MASANORI ASAKURA; NORIYUKI OTSUBO; TOMOHIDE TERASOMA
For a certain class of hypergeometric functions $_{3}F_{2}$ with rational parameters, we give a sufficient condition for the special value at $1$ to be expressed in terms of logarithms of algebraic numbers. We give two proofs, both of which are algebro-geometric and related to higher regulators.
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HASSE PRINCIPLES FOR ÉTALE MOTIVIC COHOMOLOGY Nagoya Math. J. (IF 0.556) Pub Date : 2018-12-26 THOMAS H. GEISSER
We discuss the kernel of the localization map from étale motivic cohomology of a variety over a number field to étale motivic cohomology of the base change to its completions. This generalizes the Hasse principle for the Brauer group, and is related to Tate–Shafarevich groups of abelian varieties.
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CHERN CLASSES WITH MODULUS Nagoya Math. J. (IF 0.556) Pub Date : 2019-02-01 RYOMEI IWASA; WATARU KAI
In this paper, we construct Chern classes from the relative $K$ -theory of modulus pairs to the relative motivic cohomology defined by Binda–Saito. An application to relative motivic cohomology of henselian dvr is given.
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REFINED SWAN CONDUCTORS $\text{mod}~p$ OF ONE-DIMENSIONAL GALOIS REPRESENTATIONS Nagoya Math. J. (IF 0.556) Pub Date : 2019-06-03 KAZUYA KATO; ISABEL LEAL; TAKESHI SAITO
For a character of the absolute Galois group of a complete discrete valuation field, we define a lifting of the refined Swan conductor, using higher dimensional class field theory.
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HIGHER IDELES AND CLASS FIELD THEORY Nagoya Math. J. (IF 0.556) Pub Date : 2018-10-02 MORITZ KERZ; YIGENG ZHAO
We use higher ideles and duality theorems to develop a universal approach to higher dimensional class field theory.
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MOTIVIC EULER CHARACTERISTICS AND WITT-VALUED CHARACTERISTIC CLASSES Nagoya Math. J. (IF 0.556) Pub Date : 2019-03-22 MARC LEVINE
This paper examines Euler characteristics and characteristic classes in the motivic setting. We establish a motivic version of the Becker–Gottlieb transfer, generalizing a construction of Hoyois. Making calculations of the Euler characteristic of the scheme of maximal tori in a reductive group, we prove a generalized splitting principle for the reduction from $\operatorname{GL}_{n}$ or $\operatorname{SL}_{n}$
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A CONSTRUCTION OF SURFACES WITH LARGE HIGHER CHOW GROUPS Nagoya Math. J. (IF 0.556) Pub Date : 2018-10-16 TOMOHIDE TERASOMA
In this paper, we construct surfaces in $\mathbf{P}^{3}$ with large higher Chow groups defined over a Laurent power series field. Explicit elements in higher Chow group are constructed using configurations of lines contained in the surfaces. To prove the independentness, we compute the extension class in the Galois cohomologies by comparing them with the classical monodromies. It is reduced to the
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ARITHMETIC STRUCTURES FOR DIFFERENTIAL OPERATORS ON FORMAL SCHEMES Nagoya Math. J. (IF 0.556) Pub Date : 2019-12-19 CHRISTINE HUYGHE; TOBIAS SCHMIDT; MATTHIAS STRAUCH
Let $\mathfrak{o}$ be a complete discrete valuation ring of mixed characteristic $(0,p)$ and $\mathfrak{X}_{0}$ a smooth formal $\mathfrak{o}$ -scheme. Let $\mathfrak{X}\rightarrow \mathfrak{X}_{0}$ be an admissible blow-up. In the first part, we introduce sheaves of differential operators $\mathscr{D}_{\mathfrak{X},k}^{\dagger }$ on $\mathfrak{X}$ , for every sufficiently large positive integer $k$
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ON THE CLASSIFICATION BY MORIMOTO AND NAGANO Nagoya Math. J. (IF 0.556) Pub Date : 2019-12-19 ALEXANDER ISAEV
We consider a family $M_{t}^{3}$ , with $t>1$ , of real hypersurfaces in a complex affine three-dimensional quadric arising in connection with the classification of homogeneous compact simply connected real-analytic hypersurfaces in $\mathbb{C}^{n}$ due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the Cauchy–Riemann (CR)-embeddability of $M_{t}^{3}$
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ON THE CONJECTURE OF VASCONCELOS FOR ARTINIAN ALMOST COMPLETE INTERSECTION MONOMIAL IDEALS Nagoya Math. J. (IF 0.556) Pub Date : 2019-12-10 KUEI-NUAN LIN; YI-HUANG SHEN
In this short note, we confirm a conjecture of Vasconcelos which states that the Rees algebra of any Artinian almost complete intersection monomial ideal is almost Cohen–Macaulay.
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REPETITIVE EQUIVALENCES AND TILTING THEORY Nagoya Math. J. (IF 0.556) Pub Date : 2019-12-06 JIAQUN WEI
Let $R$ be a ring and $T$ be a good Wakamatsu-tilting module with $S=\text{End}(T_{R})^{op}$ . We prove that $T$ induces an equivalence between stable repetitive categories of $R$ and $S$ (i.e., stable module categories of repetitive algebras $\hat{R}$ and ${\hat{S}}$ ). This shows that good Wakamatsu-tilting modules seem to behave in Morita theory of stable repetitive categories as that tilting modules
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VIRTUAL ALGEBRAIC FIBRATIONS OF KÄHLER GROUPS Nagoya Math. J. (IF 0.556) Pub Date : 2019-12-06 STEFAN FRIEDL; STEFANO VIDUSSI
This paper stems from the observation (arising from work of Delzant) that “most” Kähler groups $G$ virtually algebraically fiber, that is, admit a finite index subgroup that maps onto $\mathbb{Z}$ with finitely generated kernel. For the remaining ones, the Albanese dimension of all finite index subgroups is at most one, that is, they have virtual Albanese dimension $va(G)\leqslant 1$ . We show that
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EFFECTIVE CYCLES ON SOME LINEAR BLOWUPS OF PROJECTIVE SPACES Nagoya Math. J. (IF 0.556) Pub Date : 2019-12-05 NORBERT PINTYE; ARTIE PRENDERGAST-SMITH
We compute cones of effective cycles on some blowups of projective spaces in general sets of lines.
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THE SECOND FUNDAMENTAL THEOREM OF INVARIANT THEORY FOR THE ORTHOSYMPLECTIC SUPERGROUP Nagoya Math. J. (IF 0.556) Pub Date : 2019-12-04 G. I. LEHRER; R. B. ZHANG
The first fundamental theorem of invariant theory for the orthosymplectic supergroup scheme $\text{OSp}(m|2n)$ states that there is a full functor from the Brauer category with parameter $m-2n$ to the category of tensor representations of $\text{OSp}(m|2n)$ . This has recently been proved using algebraic supergeometry to relate the problem to the invariant theory of the general linear supergroup. In
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CR-HARMONIC MAPS Nagoya Math. J. (IF 0.556) Pub Date : 2019-12-02 GAUTIER DIETRICH
We develop the notion of renormalized energy in Cauchy–Riemann (CR) geometry for maps from a strictly pseudoconvex pseudo-Hermitian manifold to a Riemannian manifold. This energy is a CR invariant functional whose critical points, which we call CR-harmonic maps, satisfy a CR covariant partial differential equation. The corresponding operator coincides on functions with the CR Paneitz operator.
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A NONDEGENERATE EXCHANGE MOVE ALWAYS PRODUCES INFINITELY MANY NONCONJUGATE BRAIDS Nagoya Math. J. (IF 0.556) Pub Date : 2019-12-02 TETSUYA ITO
We show that if a link $L$ has a closed $n$ -braid representative admitting a nondegenerate exchange move, an exchange move that does not obviously preserve the conjugacy class, $L$ has infinitely many nonconjugate closed $n$ -braid representatives.
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EQUIVARIANT ${\mathcal{D}}$ -MODULES ON ALTERNATING SENARY 3-TENSORS Nagoya Math. J. (IF 0.556) Pub Date : 2019-11-29 ANDRÁS C. LŐRINCZ; MICHAEL PERLMAN
We consider the space $X=\bigwedge ^{3}\mathbb{C}^{6}$ of alternating senary 3-tensors, equipped with the natural action of the group $\operatorname{GL}_{6}$ of invertible linear transformations of $\mathbb{C}^{6}$ . We describe explicitly the category of $\operatorname{GL}_{6}$ -equivariant coherent ${\mathcal{D}}_{X}$ -modules as the category of representations of a quiver with relations, which has
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ORBIFOLD ASPECTS OF CERTAIN OCCULT PERIOD MAPS Nagoya Math. J. (IF 0.556) Pub Date : 2019-11-27 ZHIWEI ZHENG
We first characterize the automorphism groups of Hodge structures of cubic threefolds and cubic fourfolds. Then we determine for some complex projective manifolds of small dimension (cubic surfaces, cubic threefolds, and nonhyperelliptic curves of genus $3$ or $4$ ), the action of their automorphism groups on Hodge structures of associated cyclic covers, and thus confirm conjectures made by Kudla and
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HOMOGENEOUS SASAKI AND VAISMAN MANIFOLDS OF UNIMODULAR LIE GROUPS Nagoya Math. J. (IF 0.556) Pub Date : 2019-11-08 D. ALEKSEEVSKY; K. HASEGAWA; Y. KAMISHIMA
A Vaisman manifold is a special kind of locally conformally Kähler manifold, which is closely related to a Sasaki manifold. In this paper, we show a basic structure theorem of simply connected homogeneous Sasaki and Vaisman manifolds of unimodular Lie groups, up to holomorphic isometry. For the case of unimodular Lie groups, we obtain a complete classification of simply connected Sasaki and Vaisman
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