Hodge Groups of Hodge Structures with Hodge Numbers (n,0,...,0,n)

Algebraic Geometry Seminar

Laure Flapan (UCLA)

Friday, March 24, 2017 -
3:15pm to 4:15pm
Location: 
119 Physics

One of the main tools available for proving certain cases of the Hodge conjecture for abelian varieties is to compute the Hodge groups of the weight-1 Hodge structures associated to these abelian varieties. Thus Hodge groups of abelian varieties have been extensively investigated. In this talk, we discuss generalizing these results about Hodge groups to arbitrary-weight Hodge structures with Hodge numbers (n,0,…,0,n), particularly when n is prime or twice a prime. These generalizations yield some new results about Hodge classes of 2p-dimensional abelian varieties.