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