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Towards Non-Abelian $p$-adic Hodge Theory in the Good Reduction Case. Memoirs of the American Mathematical Society ; pp;.

**Table of contents**

- Bestselling Series
- 𝑝-adic Hodge Theory ()
- Bestselling Series
- A non-abelian conjecture of Tate–Shafarevich type for hyperbolic curves

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After browsing both articles I could not see how they and Faltings' article relate to each other. For example the Ogus-Vologodsky theory is with positive characteristic coefficients, whereas Olsson and the work of Faltings is with char 0 coefficients. Sign up or log in Sign up using Google.

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### Bestselling Series

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- TOWARDS NON–ABELIAN P –ADIC HODGE THEORY IN THE GOOD REDUCTION CASE;
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## 𝑝-adic Hodge Theory ()

What do you want to do in September for MO's tenth anniversary? Related Using this analysis, we prove analogues of the Shafarevich and Fontaine-Mazur finiteness conjectures for function fields over algebraically closed fields in arbitrary characteristic, and a weak variant of the Frey-Mazur conjecture for function fields in characteristic zero.

Abstract: We will compare two different constructions of p-adic L-functions for modular forms and their relationship to Galois cohomology: one using Kato? At a more technical level, we will prove the equality of two elements of a local Iwasawa cohomology group, one arising from Kato? We will show that this equality holds even in the cases when the construction of p-adic L-functions is still unknown i.

### Bestselling Series

Since then various authors have constructed eigenvarieties for automorphic forms on many other groups. This period domain admits natural stratifications, analogous to the Ekedahl-Oort and Newton stratifications from the theory of integral models. These are easy to define but difficult to describe.

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I'll give an explicit description of the Ekedahl-Oort stratification in the first nontrivial case: that of compact Shimura curves. This is joint work with Davesh Maulik and Yunqing Tang. April 1 Speaker: Evangelia Gazaki Michigan Title: A structure theorem for zero-cycles on products of elliptic curves over p-adic fields. A weaker form of this conjecture was recently established, but the general conjecture is only known for very limited classes of varieties.

## A non-abelian conjecture of Tate–Shafarevich type for hyperbolic curves

In this talk I will present some recent joint work with Isabel Leal, where we prove this conjecture for products of elliptic curves, under some assumptions on their reduction type. Our methods often allow us to obtain very sharp results about the structure of the group of zero-cycles on such products and also give us some promising global-to-local information. Abstract: We'll discuss a work in progress describing properties of p-adic L-functions of a modular form whose Galois representation is residually reducible.

This is joint work with Rob Pollack.

Abstract: In Artin-Tate constructed a canonical pairing on the Brauer group of a surface over a finite field, and conjectured it to be alternating. I will present a resolution to this conjecture, based on a new connection to Steenrod operations and other ideas originating in algebraic topology.