• Compos. Math. (IF 1.301) Pub Date : 2020-03-26
Azat M. Gainutdinov; Ingo Runkel

For ${\mathcal{C}}$ a factorisable and pivotal finite tensor category over an algebraically closed field of characteristic zero we show: (1) ${\mathcal{C}}$ always contains a simple projective object; (2) if ${\mathcal{C}}$ is in addition ribbon, the internal characters of projective modules span a submodule for the projective $\text{SL}(2,\mathbb{Z})$ -action; (3) the action of the Grothendieck ring

更新日期：2020-03-27
• Compos. Math. (IF 1.301) Pub Date : 2020-03-24
Jeremy Miller; Rohit Nagpal; Peter Patzt

We prove a representation stability result for the codimension-one cohomology of the level-three congruence subgroup of $\mathbf{SL}_{n}(\mathbb{Z})$ . This is a special case of a question of Church, Farb, and Putman which we make more precise. Our methods involve proving finiteness properties of the Steinberg module for the group $\mathbf{SL}_{n}(K)$ for $K$ a field. This also lets us give a new proof

更新日期：2020-03-24
• Compos. Math. (IF 1.301) Pub Date : 2020-03-24
Eduard Einstein; Daniel Groves

We introduce a new kind of action of a relatively hyperbolic group on a $\text{CAT}(0)$ cube complex, called a relatively geometric action. We provide an application to characterize finite-volume Kleinian groups in terms of actions on cube complexes, analogous to the results of Markovic and Haïssinsky in the closed case.

更新日期：2020-03-24
• Compos. Math. (IF 1.301) Pub Date : 2020-02-27
Sergey Mozgovoy; Olivier Schiffmann

We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus $g$ defined over a finite field, when the twisting line bundle degree is at least $2g-2$ (this includes the case of usual Higgs bundles). This yields a closed expression for the Donaldson–Thomas invariants of the moduli spaces of twisted Higgs bundles

更新日期：2020-02-27
• Compos. Math. (IF 1.301) Pub Date : 2020-02-17
John R. Doyle; Bjorn Poonen

Fix $d\geqslant 2$ and a field $k$ such that $\operatorname{char}k\nmid d$ . Assume that $k$ contains the $d$ th roots of $1$ . Then the irreducible components of the curves over $k$ parameterizing preperiodic points of polynomials of the form $z^{d}+c$ are geometrically irreducible and have gonality tending to $\infty$ . This implies the function field analogue of the strong uniform boundedness conjecture

更新日期：2020-02-18
• Compos. Math. (IF 1.301) Pub Date : 2020-02-17
Francis Bischoff; Henrique Bursztyn; Hudson Lima; Eckhard Meinrenken

Given a manifold $M$ with a submanifold $N$ , the deformation space ${\mathcal{D}}(M,N)$ is a manifold with a submersion to $\mathbb{R}$ whose zero fiber is the normal bundle $\unicode[STIX]{x1D708}(M,N)$ , and all other fibers are equal to $M$ . This article uses deformation spaces to study the local behavior of various geometric structures associated with singular foliations, with $N$ a submanifold

更新日期：2020-02-18
• Compos. Math. (IF 1.301) Pub Date : 2020-02-13
Frédéric Campana; Jean-Pierre Demailly; Thomas Peternell

We study compact complex three-dimensional manifolds with vanishing second Betti number. In particular, we show that a compact complex manifold homeomorphic to the six-dimensional sphere does carry any non-constant meromorphic function.

更新日期：2020-02-13
• Compos. Math. (IF 1.301) Pub Date : 2020-02-06
Junecue Suh

A well-known conjecture, often attributed to Serre, asserts that any motive over any number field has infinitely many ordinary reductions (in the sense that the Newton polygon coincides with the Hodge polygon). In the case of Hilbert modular cuspforms $f$ of parallel weight $(2,\ldots ,2)$ , we show how to produce more ordinary primes by using the Sato–Tate equidistribution and combining it with the

更新日期：2020-02-07
• Compos. Math. (IF 1.301) Pub Date : 2020-01-20
Nils Amend; Pierre Deligne; Gerhard Röhrle

Let $W\subset \operatorname{GL}(V)$ be a complex reflection group and $\mathscr{A}(W)$ the set of the mirrors of the complex reflections in  $W$ . It is known that the complement $X(\mathscr{A}(W))$ of the reflection arrangement $\mathscr{A}(W)$ is a $K(\unicode[STIX]{x1D70B},1)$ space. For $Y$ an intersection of hyperplanes in $\mathscr{A}(W)$ , let $X(\mathscr{A}(W)^{Y})$ be the complement in $Y$

更新日期：2020-02-06
• Compos. Math. (IF 1.301) Pub Date : 2020-01-31
Hans-Christian Herbig; Gerald W. Schwarz; Christopher Seaton

Let $K$ be a compact Lie group with complexification $G$ , and let $V$ be a unitary $K$ -module. We consider the real symplectic quotient $M_{0}$ at level zero of the homogeneous quadratic moment map as well as the complex symplectic quotient, defined here as the complexification of $M_{0}$ . We show that if $(V,G)$ is $3$ -large, a condition that holds generically, then the complex symplectic quotient

更新日期：2020-01-31
• Compos. Math. (IF 1.301) Pub Date : 2020-01-23
Jonathan Hanselman; Jacob Rasmussen; Sarah Dean Rasmussen; Liam Watson

If $Y$ is a closed orientable graph manifold, we show that $Y$ admits a coorientable taut foliation if and only if $Y$ is not an L-space. Combined with previous work of Boyer and Clay, this implies that $Y$ is an L-space if and only if $\unicode[STIX]{x1D70B}_{1}(Y)$ is not left-orderable.

更新日期：2020-01-23
• Compos. Math. (IF 1.301) Pub Date : 2020-01-21
Bertrand Lemaire; Manish Mishra

Let $F$ be a non-Archimedean local field, $G$ a connected reductive group defined and split over $F$ , and $T$ a maximal $F$ -split torus in $G$ . Let $\unicode[STIX]{x1D712}_{0}$ be a depth-zero character of the maximal compact subgroup $T$ of $T(F)$ . This gives by inflation a character $\unicode[STIX]{x1D70C}$ of an Iwahori subgroup $\unicode[STIX]{x2110}\subset T$ of $G(F)$ . From Roche [Types

更新日期：2020-01-22
• Compos. Math. (IF 1.301) Pub Date : 2020-01-17
Jørgen Vold Rennemo

We study the derived category of a complete intersection $X$ of bilinear divisors in the orbifold $\operatorname{Sym}^{2}\mathbb{P}(V)$ . Our results are in the spirit of Kuznetsov’s theory of homological projective duality, and we describe a homological projective duality relation between $\operatorname{Sym}^{2}\mathbb{P}(V)$ and a category of modules over a sheaf of Clifford algebras on $\mathbb 更新日期：2020-01-17 • Compos. Math. (IF 1.301) Pub Date : 2020-01-13 Yusuke Nakamura; Hiromu Tanaka In this paper, we establish a vanishing theorem of Nadel type for the Witt multiplier ideals on threefolds over perfect fields of characteristic larger than five. As an application, if a projective normal threefold over$\mathbb{F}_{q}$is not klt and its canonical divisor is anti-ample, then the number of the rational points on the klt-locus is divisible by$q$. 更新日期：2020-01-13 • Compos. Math. (IF 1.301) Pub Date : 2020-01-07 Pierrick Bousseau Gross, Hacking and Keel have constructed mirrors of log Calabi–Yau surfaces in terms of counts of rational curves. Using$q$-deformed scattering diagrams defined in terms of higher-genus log Gromov–Witten invariants, we construct deformation quantizations of these mirrors and we produce canonical bases of the corresponding non-commutative algebras of functions. 更新日期：2020-01-07 • Compos. Math. (IF 1.301) Pub Date : 2020-01-06 Roger Casals; Álvaro del Pino; Francisco Presas This paper contributes to the study of Engel structures and their classification. The main result introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This implies a complete$h$-principle when auxiliary data is fixed. As a corollary, we show that Lorentz and orientable Cartan prolongations are 更新日期：2020-01-06 • Compos. Math. (IF 1.301) Pub Date : 2019-12-09 Matthew Stoffregen We compute the$\text{Pin}(2)$-equivariant Seiberg–Witten Floer homology of Seifert rational homology three-spheres in terms of their Heegaard Floer homology. As a result of this computation, we prove Manolescu’s conjecture that$\unicode[STIX]{x1D6FD}=-\bar{\unicode[STIX]{x1D707}}$for Seifert integral homology three-spheres. We show that the Manolescu invariants$\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD}

更新日期：2020-01-04
• Compos. Math. (IF 1.301) Pub Date : 2019-12-18
Yusuke Sugiyama; Seidai Yasuda

We prove an analogue of Belyi’s theorem in characteristic two. Our proof consists of the following three steps. We first introduce a new notion called pseudo-tameness for morphisms between curves over an algebraically closed field of characteristic two. Secondly, we prove the existence of a ‘pseudo-tame’ rational function by showing the vanishing of an obstruction class. Finally, we construct a tamely

更新日期：2020-01-04
• Compos. Math. (IF 1.301) Pub Date : 2019-12-20
Dan Petersen

Let $X$ be a topological space. We consider certain generalized configuration spaces of points on $X$ , obtained from the cartesian product $X^{n}$ by removing some intersections of diagonals. We give a systematic framework for studying the cohomology of such spaces using what we call ‘twisted commutative dg algebra models’ for the cochains on $X$ . Suppose that $X$ is a ‘nice’ topological space, $R$

更新日期：2020-01-04
• Compos. Math. (IF 1.301) Pub Date : 2019-12-19
Lifan Guan; Ronggang Shi

For a one-parameter subgroup action on a finite-volume homogeneous space, we consider the set of points admitting divergent-on-average trajectories. We show that the Hausdorff dimension of this set is strictly less than the manifold dimension of the homogeneous space. As a corollary we know that the Hausdorff dimension of the set of points admitting divergent trajectories is not full, which proves

更新日期：2020-01-04
• Compos. Math. (IF 1.301) Pub Date : 2019-12-26
David Hansen

We prove a rigid analytic analogue of the Artin–Grothendieck vanishing theorem. Precisely, we prove (under mild hypotheses) that the geometric étale cohomology of any Zariski-constructible sheaf on any affinoid rigid space $X$ vanishes in all degrees above the dimension of $X$ . Along the way, we show that branched covers of normal rigid spaces can often be extended across closed analytic subsets,

更新日期：2020-01-04
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