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Absolute Hodge classes and the Mumford-Tate conjecture for hyperkahler manifolds

组织者

侯赛因·莫瓦萨提

演讲者

Andrey Soldatenkov

时间

2023年04月07日 21:30 至 23:00

地点

Online

线上

Zoom 559 700 6085 (BIMSA)

摘要

The Hodge conjecture implies that all Hodge cycles on a smooth complex projective variety are absolute, i.e. they remain Hodge if one conjugates the variety by an automorphism of the field of complex numbers. It was shown by Deligne that all Hodge cycles on abelian varieties are absolute, although the Hodge conjecture for abelian varieties remains open. I will present my recent results about Hodge cycles on compact hyperkahler manifolds, showing that all Hodge cycles on all known examples of such manifolds are absolute. I will also discuss the related results on the Mumford-Tate conjecture for hyperkahler manifolds.