In 1976 Ribet showed how one can use congruences between Eisenstein series and cusp forms on the group GL(2) to construct non-zero elements in class groups and as a result 2-dimensional, non-split reducible Galois representations with coefficients in finite fields. We will present a similar construction in the context of the symplectic group for a specific kind of Eisenstein series - the Klingen one. We will then discuss deformations of this Galois representation that lead to a new modularity theorem. This work is joint with Tobias Berger.
Event Date
2025-11-19
Event Time
03:15 pm ~ 04:35 pm
Event Location
Wachman 413