# Guest seminar "Arithmetic Geometry"

Time: Thursdays, 2pm-4pm

Place: SR 140 Arnimallee 7

## Talks:

Date Speaker

April 28

Angelo Vistoli (Pisa)

Title: Fundamental gerbes

May 12

Piotr Achinger (Warsaw)

Title: Wild ramification and K(pi, 1) spaces.

Abstract:  A smooth variety in characteristic zero is Zariski-locally a K(\pi,1) space, i.e. has trivial higher homotopy groups. The characteristic p variant of this is not known, we do not even know whether the affine space is a K(\pi, 1) space in positive characteristic! I will show how to reduce this question to a question related to wild ramification, which might be of independent interest, and provide partial results in this direction.

May 19

De-Qi Zhang (Singapur)

Title: Rationality of homogeneous varieties

Abstract: Let G be a connected linear algebraic group over an algebraically closed field  k, and let H be a connected closed subgroup of G. We prove that the homogeneous variety G/H is a rational variety over k whenever H is solvable, or when dim(G/H)<11 and char(k)=0. When H is of maximal rank in G, we also prove that G/H is rational if the maximal semisimple quotient of G is isogenous to a product of almost-simple groups of type A, type C (when char(k)>2), or type B_3 or G_2 (when char(k)=0). This is a joint work with C. Chin.

June 2

Evangelia Gazaki (Chicago)

Title: On a filtration of CH_0 for an abelian variety

Abstract:  Let A be an abelian variety over a field k of dimension d. In this talk I will define a decreasing filtration {F_r} of the group CH_0(A) of zero cycles modulo rational equivalence which has the property that the successive quotients are ”almost” isomorphic to some Milnortype K-groups. Rationally the filtration coincides with the motivic filtration previously considered by A. Beauville and S. Bloch. We will see that when k is a p-adic field the filtration has many interesting properties. For example, we will obtain information on the kernel of the cycle map to étale cohomology. If time permits, I will also present a conjecture about the image of local Galois symbols.

June 9

Sho Tanimoto (Copenhagen)

Title: A refinement of Manin's conjecture for Fano threefolds

Abstract: Manin's conjecture predicts the generic distribution of rational points on Fano varieties, and it has the explicit asymptotic formula in terms of geometric invariants of the underlying variety. However the original version which predicts asymptotic formulae after removing proper closed sets is wrong due to covering families of subvarieties violating compatibility of Manin's conjecture, and a possible refinement, suggested by Peyre, removes thin sets instead of closed sets. One natural question is how to choose the exceptional thin set. In this talk, I would like to address this issue using birational geometry, e.g., the minimal model program and the boundedness of log Fano varieties. This is joint work with Brian Lehmann and Yuri Tschinkel.

June 16

Tomoyuki Abe (Tokyo)

Title: Localization formula for epsilon factor of algebraic D-modules

Abstract: Beilinson's philosophy of epsilon factors roughly says that epsilon factors of a "theory" are shadow of K-theoretic property of the theory, and realized this for topological epsilon factors. D. Patel established an analogy for algebraic D-modules. Keeping in mind the future application to a conjecture of Kato and Saito on a generalization of torsion formula for epsilon factor of l-adic sheaves, we show analogous formula for algebraic D-modules using Beilinson's philosophy. This is a joint work with D. Patel.

July 7

Filippo Nuccio (Saint-Étienne)

Title: tba