Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Liu Shinan，University München
Inviter:
Title:	Local model of Shimura varieties
Time & Venue:	2019.7.4 10:45-11:45 N202
Abstract:	Let X be a projective smooth algebraic variety over \mathbb{Q}. It is conjectured that the Hasse-Weil zeta function of X has nice properties, such as an analytic continuation to the whole plane, and admitting a functional equation. When X is a Shimura variety, i.e. a moduli space of abelian varieties, the calculation of zeta function is more accessible. Indeed, to calculate the local zeta factor of X at a good prime p, i.e. when X has a smooth model over \mathbb{Z}_p, one only needs to count abelian varieties over finite fields, which can be done by using Honda-Tate theory. However, to calculate the local factor at a bad prime, one also needs to know the nearby cycle sheaf. In this talk we explain how the local model of Shimura varieties allows us to determine the nearby cycle on a Shimura variety, so to calculate its local zeta factor at bad primes. We will use the modular curve Y_0(p) as our guiding example.