Time：14:00-15:00, Wednesday, May 15 2024
Venue：E4-233
Speaker：Thomas Geisser, Rikkyo University
Title：Brauer groups and Neron-Severi groups for surfaces over finite fields
Abstract：For a smooth and proper surface over a finite field, the formula of Artin and Tate relates the behaviour of the zeta-function at $1$ to other invariants of the surface. We give a refinement which equates invariants related to the Brauer group to invariants to the Neron-Severi group. If time permits we give some applications for abelian surfaces. For example, the largest Brauer group over a field of order q=p^{2r} has order 16q, and the largest Brauer group of a supersingular abelian surface over a prime field is 36.
