Finiteness and the Tate Conjecture in Codimension 2 for K3 Squares

Abstract: Two years ago, via a refined CM lifting theory, Ito-Ito-Koshikawa proved the Tate Conjecture for squares of K3 surfaces over finite fields by reducing to Tate's theorem on the endomorphisms of abelian varieties. I will explain a different proof, which is based on a twisted version of Fourier-Mukai transforms between K3 surfaces. In particular, I do not use Tate's theorem after assuming some known properties of individual K3's. The main purpose of doing so is to illustrate Tate's insight on the connection between the Tate conjecture and the positivity results in algebraic geometry for codimension 2 cycles, through some "geometry in cohomological degree 2".

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom ID = 613 5332 8443

Password = 182269

Link = zoom.com.cn/j/61353328443?pwd=eEpaNkpCdTBER3o1eFJER2NaS29qUT09

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POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

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