A Conference in Arithmetic Algebraic Geometry in Memory of Jan Nekovář

Collection A Conference in Arithmetic Algebraic Geometry in Memory of Jan Nekovář

Organizer(s) Anna Cadoret, Wiesława Nizioł, Sarah Zerbes

Date(s) 09/10/2023 - 13/10/2023

linked URL https://indico.math.cnrs.fr/event/9977/

00:00:00 / 00:00:00

14 20

Conjectures on L-functions for varieties over function fields and their relations

By Veronika Ertl

(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.

Information about the video

Date of recording 12/10/2023
Date of publication 13/10/2023
Institution IHES
Language English
Audience Researchers, Graduate Students
Format MP4

Domain(s)

Number Theory

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