Related papers: Monodromy Groups of Supersingular Abelian Surfaces…

We prove an analogue of the Tate isogeny conjecture and the semi-simplicity conjecture for overconvergent crystalline Dieudonn\'e modules of abelian varieties defined over global function fields of characteristic $p$. As a corollary we…

We show the existence of abelian surfaces $A$ over $\mathbb{Q}_p$ having good reduction with supersingular special fibre whose associated $p$-adic Galois module $V_p(A)$ is not semisimple.

Let V be a p-adic representation of the absolute Galois group G of Q_p that becomes crystalline over a finite tame extension, and assume p odd. We provide necessary and sufficient conditions for V to be isomorphic to the Tate module V_p(A)…

We classify the filtered modules with coefficients corresponding to two-dimensional potentially semi-stable $p$-adic representations of the absolute Galois groups of $p$-adic fields under the assumptions that $p$ is odd and the coefficients…

We construct infinitely many abelian surfaces A defined over the rational numbers such that, for a prime ell <= 7, the ell-torsion subgroup of A is not isomorphic as a Galois module to the ell-torsion subgroup of its dual. We do this by…

We compute the density of the set of ordinary primes of an abelian surface over a number field in terms of the l-adic monodromy group. Using the classification of l-adic monodromy groups of abelian surfaces by Fite, Kedlaya, Rotger, and…

Let $\{\rho_{\ell}:\mathrm{Gal}_K\to\mathrm{GL}_n(\mathbb{Q}_{\ell})\}_{\ell}$ be a semisimple compatible system of $\ell$-adic representations of a number field $K$ that is arising from geometry. Let…

This paper investigates the relationship between strata of abelian differentials and various mapping class groups afforded by means of the topological monodromy representation. Building off of prior work of the authors, we show that the…

We compute the Z/\ell and \ell-adic monodromy of every irreducible component of the moduli space M_g^f of curves of genus and and p-rank f. In particular, we prove that the Z/\ell-monodromy of every component of M_g^f is the symplectic…

We prove structure theorems for the moduli stack of elliptic curves equipped with $G$-structures, where $G$ is a finite 2-generated metabelian group. In particular, we show that if $G$ has exponent $e$, then there is a subgroup $H\le…

Let $G$ be a connected reductive group over a $p$-adic local field $F$. We propose and study the notions of $G$-$\varphi$-modules and $G$-$(\varphi,\nabla)$-modules over the Robba ring, which are exact faithful $F$-linear tensor functors…

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…

Let $q$ be an odd power of a prime $p\in \mathbb{N}$, and $\mathrm{PPSP}(\sqrt{q})$ be the finite set of isomorphism classes of principally polarized superspecial abelian surfaces in the simple isogeny class over $\mathbb{F}_q$…

The purpose of this paper is to prove a local p-adic monodromy theorem for ordinary abelian surfaces and K3 surfaces with bad reduction in characteristic p. As an application, we get a finiteness result for the reduction of their Hecke…

We study topological aspects of supersolvable abelian arrangements, toric arrangements in particular. The complement of such an arrangement sits atop a tower of fiber bundles, and we investigate the relationship between these bundles and…

We complement Catanese's results on isotrivially fibred surfaces by completely describing the components containing an isotrivial surface with monodromy group $\ZZ/2\ZZ$. We also give an example for deformation equivalent isotrivial…

We prove the semisimplicity conjecture for A-motives over finitely generated fields K. This conjecture states that the rational Tate modules V_p(M) of a semisimple A-motive M are semisimple as representations of the absolute Galois group of…

Let $\rho$ be a finite-dimensional faithful representation of a semisimple algebraic group $G$. By means of a deformation argument, we show that there exists a family of Abelian varieties over a smooth and projective curve over the…

Here we show that, given a finite homological system $({\cal P},\leq,\{\Delta_u\}_{u\in {\cal P}})$ for a finite-dimensional algebra $\Lambda$ over an algebraically closed field, the category ${\cal F}(\Delta)$ of $\Delta$-filtered modules…

In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some…