A Conference in Arithmetic Algebraic Geometry in Memory of Jan Nekovář

Conjectures on L-functions for Varieties Over Function Fields and Their Relations

12 oct. 2023, 11:15

1h

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Orateur

Prof. Veronika Ertl (Universitat Regensburg)

Description

(Joint work with T. Keller, Groningen, and Y. Qin, Berkeley)

We consider versions for smooth varieties $X$ over finitely generated fields $K$ in positive characteristic p of several conjectures that can be traced back to Tate, and study their interdependence. In particular, let $A/K$ be an abelian variety. Assuming resolutions of singularities in positive characteristic, I will explain how to relate the BSD-rank conjecture for $A$ to the finiteness of the $p$-primary part of the Tate-Shafarevich group of $A$ using rigid cohomology. Furthermore, I will discuss what is needed for a generalisation.

Documents de présentation

Vidéo