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CONFERENCE
Arithmetic Geometry, Representation Theory and Applications 

June 22 – 26, 2015
This conference that will punctuate the end of the ANR program p-adic Hodge theory and beyonds (ThéHopaD) aims to give an overview of some of the most striking results in arithmetic geometry with an emphasis on p-adic aspects.  We would like to cover the following topics :

  • p-adic Hodge theory and beyond.
    We will cover both arithmetic and geometric aspects of p-adic Hodge theory by focusing on some of the deepest and most challenging questions: the p-adic Langlands program for the arithmetic side and the p-adic Simpson correspondence and the theory of perfectoids for the geometric side.

  • Shimura varieties, Galois representations.
    It is well known that the cohomology of Shimura varieties provides extremely instructive examples of Galois representations. In some cases, it even allows to realize the l-adic Langlands correspondence, giving hints for the elaboration of the p-adic variant by considering the completed p-adic étale cohomology. Two spectacular breakthroughs in this area have occured recently that will be covered during the conference. These are the result of works by Harris, Lan, Taylor and Thorne on one side and Scholze on another.

  • Ramification theory.
    The third theme of the conference will be devoted to the recent breakthroughs in the ramification theory developed by Abbes and Saito, whose leitmotiv is to kill ramification by blowing-up. Particular emphasis will be given to the recent works of Saito that aim at defining the characteristic cycle of a constructible l-adic étale sheaf on a smooth variety defined over a perfect field of characteristic p (different from l), ramified along a divisor, as a cycle in the cotangent bundle of the variety.
Scientific & Organizing Committee

Ahmed Abbes (IHÉS)
Christophe Breuil (Université Paris-Sud)
Gaëtan Chenevier (Ecole polytechnique)
Takeshi Saito (University of Tokyo)

Speakers

  • A. Beilinson (University of Chicago)

The Singular Support of a Constructible Sheaf

Construction of Torsion Galois Representations

Non-Minimal Modularity Lifting Theorems for Imaginary Quadratic Fields

The Category MF in the Semistable Case

  • T. Gee (Imperial College London)

Moduli Stacks of Potentially Barsotti-Tate Galois Representations

Construction of p-adic L-Functions for Unitary Groups

  • D. Helm (Imperial College London)

Whittaker Models, Converse Theorems and the Local Langlands Correspondence for GL_n in Families

On de Rham Lifts of Local Galois Representations

Affinoids in the Lubin-Tate Perfectoid Space and Simple Epipelagic Representations

Honda-Tate Theory for Shimura Varieties

  • K. Nakamura (Hokkaido University)

Local Epsilon Isomorphisms for Rank Two p-adic Representations of Gal(\bar{Q}_p/Q_p) and a Functional Equation of Kato’s Euler Systems

The Characteristic Cycle and the Singular Support of an Etale Sheaf

The Witt Vector Affine Grassmannian

  • B. Schraen (Université de Versailles Saint-Quentin-en-Yvelines)

Classicality on Eigenvarieties

Galois Representations in the Cohomology of Shimura Varieties

  • Y. Tian (Morningside Center for Mathematics, Beijing)

Generic Tate Cycles on Certain Unitary Shimura Varieties Over Finite Fields

  • T. Tsuji (University of Tokyo)

On p-adic Etale Cohomology of Perverse Sheaves