Related papers: Specialization of Difference Equations and High Fr…

We continue the work of Kaplansky on immediate valued field extensions and determine special properties of elements in such extensions. In particular, we are interested in the question when an immediate valued function field of…

We study Frobenius eigenvalues of the compactly supported rigid cohomology of a variety defined over a finite field of $q$ elements via Dwork's method. A couple of arithmetic consequences will be drawn from this study. As the first…

We study certain mild degenerations of algebraic varieties which appear in the analysis of a large class of supersymmetric theories, including superstring theory. We analyze Witten's sigma-model and find that the non-transversality of the…

Let X be a separated scheme of finite type over an algebraically closed field k and let m be a natural number. By an explicit geometric construction using torsors we construct a pairing between the first mod m Suslin homology and the first…

We give a categorical description of all abelian varieties with commutative endomorphism ring over a finite field with $q=p^a$ elements in a fixed isogeny class in terms of pairs consisting of a fractional $\mathbb Z[\pi,q/\pi]$-ideal and a…

The paper deals with Henselian valued field with analytic structure. Actually, we are focused on separated analytic structures, but the results remain valid for strictly convergent analytic ones as well. A classical example of the latter is…

Let G be a Lie group over a local field of positive characteristic which admits a contractive automorphism f (i.e., the forward iterates f^n(x) of each group element x converge to the neutral element 1). We show that then G is a torsion…

We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties.…

This article concerns properties of mixed $\ell$-adic complexes on varieties over finite fields, related to the action of the Frobenius automorphism. We establish a fiberwise criterion for the semisimplicity and Frobenius semisimplicity of…

We show that conjugation by an automorphism of the complex numbers (as an abstract field) may change the topological fundamental group of a locally symmetric variety over C. As a consequence, we obtain a large class of algebraic varieties…

Let $K$ be a number field. We present several new finiteness results for isomorphism classes of abelian varieties over $K$ whose $\ell$-power torsion fields are arithmetically constrained for some rational prime $\ell$. Such arithmetic…

We develop a categorical and algebro-geometric treatment of localization for cohomological theories endowed with an open--closed recollement. Starting from a class on a space whose restriction to the open complement vanishes, we show that…

Let $A$ be an abelian variety over a number field $\mathrm E\subset \mathbb C$ and let $\mathbf G$ denote the Mumford--Tate group of $A$. After replacing $\mathrm E$ by a finite extension, the action of the absolute Galois group…

In this paper we provide a wildness criterion for any finite dimensional Hopf algebra with finitely generated cohomology. This generalizes a result of Farnsteiner to not necessarily cocommutative Hopf algebras over ground fields of…

We introduce and study the filtration on the space of automorphic functions (in the everywhere unramified situation for the function field case) obtained by transferring the filtration on the spectral side of the classical Langlands…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

We introduce a class of theories called metastable, including the theory of algebraically closed valued fields (ACVF) as a motivating example. The key local notion is that of definable types dominated by their stable part. A theory is…

Suppose $F$ is either a global field or a finitely generated extension of ${\mathbf Q}$, $A$ is an abelian variety over $F$, and $\ell$ is a prime not equal to the characteristic of $F$. Let $Z$ denote the center of the endomorphism algebra…

We show that separably closed valued fields of finite imperfection degree (either with lambda-functions or commuting Hasse derivations) eliminate imaginaries in the geometric language. We then use this classification of interpretable sets…

We construct normal hypersurfaces whose local cohomology modules have infinitely many associated primes. These include unique factorization domains of characteristic zero with rational singularities, as well as F-regular unique…