A new approach to p-adic modular foms
Vortrag von Prof. Dr. Fabrizio Andreatta
Datum: 07.10.13 Zeit: 13.15 - 14.45 Raum: Y27H25
Classical elliptic modular forms can be seen geometrically as sections of powers of the cotangent bundle of modular curves. So far this was not the case for $p$-adic modular forms. Their weight is a $p$-adic number and $p$-adic powers of sheaves do not make sense.... I will present a new approach to the problem, in collaboration with A. Iovita and G. Stevens, which allows to define $p$-adic modular forms in a very geometric fashion as sections of line bundles. This has the advantage of being well suited for generalization to higher dimensional Shimura varieties (namely Siegel and Hilbert modular varieties) where a good theory of $p$-adic modular forms has been lacking so far.