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

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.

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