Producing Geometric Deformations of Orthogonal and Symplectic Galois Representations

Abstract

For a representation of the absolute Galois group of the rationals over a finite field of characteristic $p$, we study the existence of a lift to characteristic zero that is geometric in the sense of the Fontaine-Mazur conjecture. For two-dimensional representations, Ramakrishna proved that under technical assumptions odd representations admit geometric lifts. We generalize this to higher dimensional orthogonal and symplectic representations. A key step is generalizing and studying a local deformation condition at $p$ arising from Fontaine-Laffaille theory.

This is one piece of the earlier submission which was split for publication

Cited by in corpus (5)

• G-valued local deformation rings and global lifts
• Minimally Ramified Deformations when $\ell \ne p$
• Quantitative level lowering for Galois representations
• Deformation of rigid conjugate self-dual Galois representations
• A Refined Lifting Theorem for Supersingular Galois Representations