Eichler-Shimura morphisms for GSp_4. The holomorphic case I

Atelier: Théorie de Coleman supérieure et applications / Workshop: Higher Coleman theory and applications (8 déc. 2020 / Dec. 8, 2020)

Fabrizio Andreatta (Universita Statale di Milano, Italy)

Abstract: In these two talks I will introduce on the SIegel threefold:
1) etale p-adic coefficients whose cohomology groups admit slope decomposition and provide p-adic families of global Galois representation.
2) overconvergent de Rham p-adic coefficients whose cohomology admit slope decomposition
3) a comparison between the two in the spirit of the classical Eichler-Shimura isomorphisms
I will consider two settings, one of which fits in the context of higher Coleman theory. A generalization of the BGG complex in this setting will be introduced and studied.