Sections of a conic bundle and motivic fibered zeta function
Speaker: Đào Văn Thịnh (BICMR -- Beijing)

Time: 9:30 - 10:30, Wednesday January 19th, 2022.

Abstract: In this talk, I will present the first step in comparing the density of some "special" sections of a conic bundle with a special value of a zeta function. More precisely, given a conic bundle E over P^1xP^1, the product of two projective lines, with the associated discriminant curve D. In order to understand some sections from the (first or second) P^1 to E, we first need to consider some sections from that P^1 to P^1xP^1 and see how they interact with D (such as having transversal intersection,...). It turns out that at this step, we can express the density of sections satisfying a given property (an interaction with D) in terms of a special value of a (motivic) fibered zeta function. Notice that if we work with finite fields, we also obtain a "normal" zeta function, but the methods used (over finite fields and arbitrary fields) are different.

Online: https://meet.google.com/esi-huxm-xqg