Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	杨梓诠博士，University of Wisconsin–Madison
Inviter:
Title:	Arithmetic Deformation of Line Bundles
Language:	Chinese
Time & Venue:	2023.09.21 09:00-10:00 腾讯会议：587-534-625 密码：0921
Abstract:	In this talk, I address the following question: In an arithmetic family, can we obtain every line bundle in characteristic p by specializing those in characteristic zero? I will first explain that, when h^{2,0} = 1, being able to answer this questionhas important applications to the Tate/BSD conjecture, as a continuation of the previous talk. Then I will discuss a generalization when h^{2, 0} > 1. The main theorem is that, as long as the family has sufficiently big monodromy and Kodaira-Spencer map, thequestion generically has a positive answer. Examples include general hypersurface in P^3 or an elliptic surface over P^1. The method involves an application of theAx-Schanuel theorem in Hodge theory, recently established by Tsimerman and Baker. This generalization is based on a joint work with David Urbanik.