Étale fundamental groups of affinoid $p$-adic curves

Comparison of some quotients of fundamental groups of algebraic curves over p-adic fields

Cycle Classes for p - Adic Étale Tate Twists and the Image of p - Adic Regulators

In this paper, we construct Chern class maps and cycle class maps with values in p-adic étale Tate twists [Sa2]. We also relate the p-adic étale Tate twists with the finite part of Bloch-Kato. As an application, we prove that the integral part of p-adic regulator maps has values in the finite part of Galois cohomology under certain assumptions. 2000 Mathematics Subject Classification: Primary 1...

p-ADIC UNIFORMIZATION OF CURVES

Let us presume that we have at our disposal the fully-formed theory of rigidanalytic spaces., as sketched in my last talk. Why would we care to look for uniformizations of algebraic objects in the rigid analytic category? Let’s look at the analogous situation in the complex-analytic category. We know that, for example, abelian varieties are uniformized by spaces of the form C/Λ, where Λ is a fr...

On pro-p fundamental groups of marked arithmetic curves

Let k be a global field, p an odd prime number different from char(k) and S, T disjoint, finite sets of primes of k. Let GTS (k)(p) = G(k T S (p)|k) be the Galois group of the maximal p-extension of k which is unramified outside S and completely split at T . We prove the existence of a finite set of primes S0, which can be chosen disjoint from any given set M of Dirichlet density zero, such tha...

p-adic Hurwitz groups

Herrlich showed that a Mumford curve of genus g > 1 over the p-adic complex field Cp has at most 48(g− 1), 24(g− 1), 30(g− 1) or 12(g− 1) automorphisms as p = 2, 3, 5 or p > 5. The Mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p-adic triangle groups ∆p for p ≤ 5, or in a p-adic quadrangle group p for p > 5. The finite groups attaining these...