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Geometry, Arithmetic and Differential Equations of Periods
Absolute Hodge classes and the Mumford-Tate conjecture for hyperkahler manifolds
Absolute Hodge classes and the Mumford-Tate conjecture for hyperkahler manifolds
Organizer
Hossein Movasati
Speaker
Andrey Soldatenkov
Time
Friday, April 7, 2023 9:30 PM - 11:00 PM
Venue
Online
Online
Zoom 559 700 6085
(BIMSA)
Abstract
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.