Venue: MCM110
Title: De Rham-Betti Group of Simple Type IV abelian fourfolds
Abstract: De Rham-Betti Structure of an abelian variety A defined over \bar{Q} consists of the triple: its first singular cohomology group with Q coefficients, its first algebraic deRham cohomology group and the Grothendieck comparison isomorphism. DeRham-Betti group of A is the Tannakian fundamental group associated with such structure. It contains rich information about algebraic relations among periods of the abelian varieties. Grothendieck period conjecture is one notable example of this formalism. In this talk we will explore properties of the deRham-Betti group of abelian varieties of Type IV in the Albert classification. In particular, we show that the DeRham-Betti group of certain cases of type IV abelian fourfolds (for example simple CM abelian fourfolds) coincides with the Mumford-Tate group, thus verifying GPC in these cases. If time permitted, I will also point out difficulties in determining the dRB group for other cases. The results are part of my PhD thesis.
