T. Abe (Kavli IPMU)
Title : Ramification theory and homotopies
Abstract : I will report on the on-going project with D. Patel on characteristic cycles and epsilon factors. A goal of our project is to establish the theory of epsilon factors in the l-adic setting. I will talk about out strategy, and explain a result which is expected to play an important role in the construction of local epsilon factor.

A. Beilinson (University of Chicago)
Title : The characteristic cycle of an étale sheaf and purely inseparable maps: some examples
Abstract : The category of étale sheaves on a variety X in characteristic p does not change if we replace X by its inseparable covering. However the cotangent bundle to X changes, and one can try to understand what happens with the characteristic cycle of a given sheaf. I will discuss some examples.

K. Česnavičius (CNRS, Université Paris-Sud)
Title : Cohomological purity in bad characteristics
Abstract : An fppf cohomological purity conjecture predicts that for a regular (or, more generally, complete intersection) Noetherian local ring (R, m) and a commutative finite flat R-group scheme G, one should have H^i_m(R, G) = 0 for i < dim(R). I will discuss several cases of this conjecture. The talk is based on joint work with Peter Scholze.

L. Fargues (CNRS & Institut de Mathématiques de Jussieu)
Title : A Jacobian criterion of smoothness for algebraic diamonds
Abstract : (joint work with Peter Scholze) In our joint work with Scholze we need to give a meaning to statements like "the stack of principal G-bundles on the curve is smooth of dimension 0" and construct "smooth perfectoid charts on it". The problem is that in the perfectoid world there is no infinitesimals and thus no Jacobian criterion that would allow us to define what is a smooth morphism. The good notion in this setting is the one of a cohomologically smooth morphism, a morphism that satisfies relative Poincaré duality. I will explain a Jacobian criterion of cohomological smoothness for moduli spaces of sections of smooth algebraic varieties over the curve that allows us to solve our problems.

J. Fresán (École polytechnique)
Title : Symmetric powers of Kloosterman sums
Abstract : We construct motives associated with symmetric powers of Kloosterman sums and determine their completed L-functions, thus confirming numerical observations by Broadhurst and Roberts. Although the motives in question are ?classical?, the strategy consists in realising them first as exponential motives and computing the Hodge numbers by means of the irregular Hodge filtration. Joint work with Claude Sabbah and Jeng-Daw Yu.

O. Gabber (CNRS & IHÉS)
Title : Remarks on vanishing cycles and comparison of oriented products and rigid toposes
Abstract : TBA

Q. Guignard (ENS & IHÉS)
Title : Geometric local epsilon factors
Abstract : We propose a cohomological definition à la Laumon of local epsilon factors for l-adic local systems on the spectrum of A((T)), where A is a perfect F_p-algebra. These are graded superlines depending functorially on A, on which the trace of the Frobenius endomorphism, when A is a finite field, coincide with the local epsilon factors defined by Langlands and Deligne.
We will study various properties of these geometric local epsilon factors, notably the compatibility with induction. If time permits, we will discuss the case of mixed characteristic local fields.

H. Hu (MPIM, Bonn)
Title : Ramification bound of vanishing cycles of l-adic sheaves
Abstract : In this talk, we discuss an application of the ramification theory for l-adic sheaves on positive characteristic varieties due to Abbes, Beilinson, and Saito to studying the bound of ramification slopes of the vanishing cycle of an l-adic sheaf on a smooth fibration ramified along a vertical divisor over a base of dimension 1. We apply the boundedness proposition to an l-adic analogue of Tsuzuki's constancy of Newton polygons of F-isocrystals on Abelian varieties. This is a joint work with J.-B. Teyssier.

K. Kato (University of Chicago)
Title : Refined Swan conductors of one-dimensional Galois representations
Abstract : We define a refinement of the previously known refined Swan conductor of a one-dimensional Galois representation of a complete discrete valuation field, by using higher dimensional class field theory. This is a joint work with Isabel Leal and Takeshi Saito.

T. Koshikawa (RIMS)
Title : CM liftings of K3 surfaces and the Tate conjecture
Abstract : I will explain that any K3 surface of finite height over a finite field admits a CM lifting (after extending the base field). In fact, one can control the CM action on the lifting. This has an application to the Tate conjecture for the square of the K3 surface. Our work is largely influenced by the works of Nygaard-Ogus and Madapusi Pera on the Tate conjecture for the K3 surface itself, and the Kuga-Satake construction plays a key role. Joint work with Kazuhiro Ito and Tetsushi Ito.

M. Morrow (CNRS & Institut de Mathématiques de Jussieu)
Title : Coefficients in integral p-adic Hodge theory
Abstract : Joint with Takeshi Tsuji. Given a smooth scheme over the ring of integers of a p-adic field, we study certain coefficient systems which live in the pro-étale site of its generic fibre and are closely related to Faltings' small generalised representations. Each such coefficient system simultaneously encodes a lisse étale sheaf, a module with flat connection, and a crystal, whose cohomologies are then intertwined by a relative form of the A_{inf} cohomology introduced in "Integral p-adic Hodge theory" by Bhatt-M-Scholze. Some relations to an integral form of Faltings' p-adic Simpson's correspondence may also be discussed.

M. Olsson (UC Berkeley)
Title : Specialization of fundamental groups for log schemes
Abstract : I will discuss various results about specialization maps for fundamental groups of log schemes. In particular explain an étale analog of a result of Nakayama and Ogus on variation of fundamental groups in families.

F. Orgogozo (CNRS & École polytechnique)
Title : Deligne's geometrical approach to the product formula for l-adic epsilon factors
Abstract : Around 1985, Gérard Laumon gave a proof of the local factorization of the determinant of the Frobenius map acting on the cohomology of a curve. Shortly before Laumon's work, however, Deligne had developed a different approach to the problem, which is not well known today. In this talk, I would like to introduce Deligne's method to a wider audience, in the hope that its full potential has yet to be exploited. Its starting point is Deligne's symmetric Künneth formula and the acyclicity properties of the Abel-Jacobi morphism, which led to the first proof of the result in the tame case. (Understanding Deligne's method is one part of an ongoing project with Joël Riou.)

S. Saito (University of Tokyo)
Title : Rigid analytic K-theory and p-adic Chern character
Abstract : Download the abstract

A. Shiho (University of Tokyo)
Title : On de Jong conjecture
Abstract : de Jong conjecture, which is a p-adic version of Gieseker conjecture (theorem of Esnault-Mehta), predicts that any isocrystal on a geometrically simply connected projective smooth variety over a perfect field of characteristic p>0 would be constant. I will report some results related to this conjecture. Joint work with Hélène Esnault.

E. Yang (Universität Regensburg)
Title : Twist formula of epsilon factors of constructible étale sheaves
Abstract : Using Beilinson and T. Saito's theory, we prove a twist formula for the epsilon factor of a constructible sheaf on a projective smooth variety over a finite field. This formula is a modified version of a conjecture by Kato and T. Saito. We also propose a relative version of the twist formula and discuss some applications. This is a joint work with Naoya Umezaki and Yigeng Zhao.

T. Yasuda (Tohoku University)
Title : Motivic mass formulae for formal torsors
Abstract : I will talk about motivic formulae for weighted counts of torsors over a formal punctured disk in positive characteristic with respect to a finite group. Tonini and I recently proved that such motivic counts can be indeed defined. To do so, we need to first construct the moduli space of torsors by generalizing a result of Harbater, then prove local constructibility of the weighting function. In a special case, we proved a formula for this motivic count, which can be regarded as the motivic version of Bhargava's mass formula. If time permits, I will also explain relation of this counting problem with singularities from the viewpoint of the minimal model program. This is a joint work with Fabio Tonini.

Y. Yatagawa (University of Saitama)
Title : Characteristic cycle of a rank 1 sheaf and ramification theory
Abstract : The singular support and the characteristic cycle of a constructible sheaf on a smooth variety are defined by A. Beilinson and T. Saito using vanishing cycles. We study a few relations between the characteristic cycle and the wild ramification of a sheaf, and give an explicit computation of the singular support and the characteristic cycle of a rank 1 sheaf on a surface using ramification theory.

W. Zheng (Morningside Center of Mathematics)
Title : Nearby cycles over general bases and duality
Abstract : Over one-dimensional bases, Gabber and Beilinson proved theorems on the commutation of the nearby cycle functor and the vanishing cycle functor with duality. In this talk, I will explain a way to unify the two theorems, confirming a prediction of Deligne. I will also discuss the case of higher-dimensional bases and applications to local acyclicity, following suggestions of Illusie and Gabber. This is joint work with Qing Lu.