Tate and Mumford-Tate conjectures for surfaces of general type with p_g=q=2

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
Ore: 16:30

Relatore:

• Matteo Penegini (Università di Genova)

Abstract:

In this talk we discuss the cohomology of smooth projective complex surfaces S  of general type with invariants p_g = q = 2 and surjective Albanese morphism.
We show that on a Hodge-theoretic level, the cohomology is described  by the cohomology of the Albanese variety and a K3 surface X  that we call the K3 partner of S.
Furthermore, we show that in suitable cases we can geometrically construct the K3 partner X and an algebraic correspondence in S x X that relates the cohomology of S and X.
Finally, we prove the Tate and Mumford-Tate conjectures for those surfaces S that lie in connected components of the Gieseker moduli space that contain a product-quotient surface.

Referente: Roberto Pignatelli