Explicit reduction modulo $p$ of certain crystalline representations

Abstract

We use the p-adic local Langlands correspondence for GL_2(Q_p) to explicitly compute the reduction modulo p of crystalline representations of small slope, and give applications to modular forms.

10 pages, appeared in IMRN 2009, no. 12. This version does not incorporate any minor changes (e.g. typographical changes) made in proof