Explicit reduction modulo p of certain 2-dimensional crystalline representations, II

TL;DR

This paper completes the calculation of the reduction modulo p of certain 2-dimensional crystalline G_{Q_p} representations with slope less than 1, utilizing the p-adic local Langlands correspondence for GL2(Q_p).

Contribution

It provides a complete description of the modulo p reduction for these representations, extending previous partial results.

Findings

Complete description of reduction modulo p for the specified representations

Utilizes p-adic local Langlands correspondence for GL2(Q_p)

Focuses on representations with slope less than 1, p > 2

Abstract

We complete the calculations begun in [BG09], using the p-adic local Langlands correspondence for GL2(Q_p) to give a complete description of the reduction modulo p of the 2-dimensional crystalline representations of G_{Q_p} of slope less than 1, when p > 2.