Time：10:00-11:30, Tuesday, May 14, 2024
Venue：E4-233
Host:Yigeng Zhao, ITS
Speaker：Thomas Geisser, Rikkyo University
Biography:Thomas Geisser is a Professor at Rikkyo University, Tokyo, Japan. He graduated from the University of Münster with a PhD in 1994 under the supervision of Christopher Deninger. He works in the field of arithmetic geometry, motivic cohomology and algebraic K-theory. He was the recipient of the Sloan Fellowship 2000 and the Alexander von Humboldt Research Award 2021.
Title：Weil etale cohomology and applications
Abstract:It is well known that l-adic cohomology does not yield good cohomology with integral coefficients. In the early 2000s, Lichtenbaum proposed the definition of cohomology groups, called Weil-etale cohomology, with better properties. We explain the definition of Weil-etale cohomology for varieties over finite fields, and its relationship to etale cohomology. As applications we discuss how Weil-etale cohomology allows nicer formulas for special values of zeta-functions over finite fields, and for the Birch and Swinnerton-Dyer conjecture over function fields.
