Unobstructed deformation problems for GSp(4)

TL;DR

This paper demonstrates that for many cuspidal automorphic representations of GSp(4), the local obstructions to deforming associated residual Galois representations generally disappear, simplifying deformation theory analysis.

Contribution

It establishes the generic vanishing of local obstructions in the deformation theory of residual Galois representations linked to GSp(4) automorphic forms.

Findings

Local obstructions vanish for many GSp(4) automorphic representations

Simplifies deformation theory for residual Galois representations

Provides new insights into automorphic Galois deformation problems

Abstract

We prove, for many cuspidal automorphic representations for GSp(4), that the local obstructions to the deformation theory of the associated residual Galois representations generically vanish.