BIMSA >
BIMSA-YMSC Tsinghua Number Theory Seminar
The Tate conjecture over finite fields for varietes with
The Tate conjecture over finite fields for varietes with
组织者
刁晗生
, 胡悦科
, 埃马纽埃尔·勒库图里耶
,
凯撒·鲁普
演讲者
Ziquan Yang
时间
2022年09月20日 10:00 至 11:00
地点
1118
线上
Zoom 293 812 9202
(BIMSA)
摘要
The past decade has witnessed a great advancement on the Tate conjecture for varietes with Hodge number . Charles, Madapusi-Pera and Maulik completely settled the conjecture for K3 surfaces over finite fields, and Moonen proved the Mumford-Tate (and hence also Tate) conjecture for more or less arbitrary varietes in characteristic .
In this talk, I will explain that the Tate conjecture is true for mod reductions of complex projective when , under a mild assumption on moduli. By refining this general result, we prove that in characteristic the BSD conjecture holds true for height elliptic curve over a function field of genus , as long as is subject to the generic condition that all singular fibers in its minimal compactification are irreducible. We also prove the Tate conjecture over finite fields for a class of surfaces of general type and a class of Fano varieties. The overall philosophy is that the connection between the Tate conjecture over finite fields and the Lefschetz -theorem over is very robust for varietes, and works well beyond the hyperkahler world. This is a joint work with Paul Hamacher and Xiaolei Zhao.