3 papers
math.AG2020
Classification of Kuga fiber varieties
Salman Abdulali
We complete Satake's classification of Kuga fiber varieties by showing that if a representation of a hermitian algebraic group satisfies Satake's necessary conditions, then som…
math.AG2006
Hodge structures of CM-type
Salman Abdulali
We show that any effective Hodge structure of CM-type occurs (without having to take a Tate twist) in the cohomology of some CM abelian variety over C. As a consequence we get a si…
math.AG2004
Hodge structures on abelian varieties of type III
Salman Abdulali
We show that the usual Hodge conjecture implies the general Hodge conjecture for certain abelian varieties of type III, and use this to deduce the general Hodge conjecture for all…