Related papers: On arithmetic families of filtered phi-modules and…

We prove that the image of the lifted period map on the universal cover lies in a complex Euclidean space. We also prove that the Teichm\"uller spaces of a class of polarized manifolds have complex affine structures.

Motives and automorphic forms of arithmetic type give rise to Galois representations that occur in {\it compatible families}. These compatible families are of p-adic representations with p varying. By reducing such a family mod p one…

Let $p$ be a prime. This papers aims at investigating sheaf cohomology of a broader class of $p$-adic period domains, other then the Drinfeld's upper half space (cf. \cite{O2}). Concretely, we let $\mathbf{G}$ be a split connected reductive…

Let K be a finite unramified extension of Q_p. We parametrize the (phi, Gamma)-modules corresponding to reducible two-dimensional mod p representations of G_K and characterize those which have reducible crystalline lifts with certain…

We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.

Let $K$ be a function field of characteristic $p\geq0$ or a number field over which the $abc$ conjecture holds, and let $\phi(x)=x^d+c \in K[x]$ be a unicritical polynomial of degree $d\geq2$ with $d \not\equiv 0,1\pmod{p}$. We completely…

I extend the definitions of schemes relative to monoids with zero - and therefore, toric geometry - to the world of formal schemes. This expands the usual framework to include, for instance, models for Mumford's degenerating Abelian…

In this paper we continue the study of locally analytic representations of a $p$-adic Lie group $G$ in vector spaces over a spherically complete non-archimedean field $K$, building on the algebraic approach to such representations…

We present an algorithm to determine if the $L$-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and…

We compute syntomic cohomology of semistable affinoids in terms of cohomology of $(\varphi,\Gamma)$-modules which, thanks to work of Fontaine-Herr, Andreatta-Iovita, and Kedlaya-Liu, is known to compute Galois cohomology of these affinoids.…

The Galois representation associated to a p-divisible group over a complete noetherian normal local ring with perfect residue field is described in terms of its Dieudonn\'e display. As a corollary we deduce in arbitrary characteristic…

In this paper we will introduce a certain type of morphisms of log schemes (in the sense of Fontaine, Illusie, and Kato) and investigate their moduli. Then by applying this we define a notion of toric algebraic stacks over arbitrary…

We study toric varieties over a field k that split in a Galois extension K/k using Galois cohomology with coefficients in the toric automorphism group. Part of this Galois cohomology fits into an exact sequence induced by the presentation…

Let $G$ be a split reductive group over the ring of integers in a $p$-adic field with residue field $\mathbf{F}$. Fix a representation $\overline{\rho}$ of the absolute Galois group of an unramified extension of $\mathbf{Q}_p$, valued in…

The aim of this paper is to study the structure of the higher-dimensional Teichm\"uller and Riemann moduli spaces, viewed as stacks over the category of complex manifolds. We first show that the space of complex operators on a smooth…

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…

In this note, we prove the logarithmic $p$-adic comparison theorem for open rigid analytic varieties. We prove that a smooth rigid analytic variety with a strict simple normal crossing divisor is locally $K(\pi,1)$ (in a certain sense) with…

Given a global field K and a rational function phi defined over K, one may take pre-images of 0 under successive iterates of phi, and thus obtain an infinite rooted tree T by assigning edges according to the action of phi. The absolute…

This paper concerns arithmetic families of $\varphi$-modules over reduced affinoid spaces. For such a family, we first prove that the slope polygons is lower semicontinuous around any rigid point. If the slope polygons are locally constant…

In this paper, we define and construct canonical filtered $F$-crystals with $G$-structure over the integral models for Shimura varieties of abelian type at hyperspecial level defined by Kisin. We check that these are related by $p$-adic…