A Note on Potential Diagonalizability of Crystalline Representations

TL;DR

This paper proves that all crystalline Galois representations over an unramified extension with certain Hodge-Tate weights are potentially diagonalizable, advancing understanding of their structure in p-adic Hodge theory.

Contribution

It establishes the potential diagonalizability of all crystalline representations with restricted Hodge-Tate weights over unramified extensions, a new result in p-adic Hodge theory.

Findings

All crystalline representations with weights in {0,..., p-1} are potentially diagonalizable.

The result applies to Galois groups of unramified extensions of Q_p.

Provides new insights into the structure of crystalline Galois representations.

Abstract

Let K_0 be a finite unramified extension of Q_p. We show that all crystalline representations of G_{K_0} (the absolute Galois group of K_0) with Hodge-Tate weights in {0, ..., p-1} are potentially diagonalizable.