4/30/2009

Claus Sorensen
Princeton University

Symplectic Galois representations over totally real fields.

We associate p-adic Galois representations to globally generic cusp forms on GSp(4), over a totally real field, with a Steinberg component at some finite place. At places v not dividing p one has local-global compatibility, the local correspondence being that defined by Gan and Takeda. In particular, the rank of the monodromy operator at such a place v is determined by the level of the v-component of the cusp form. Moreover, the Swan conductor is essentially the depth.