Unobstructed Galois deformation problems associated to GSp(4)

Abstract: To a cuspidal automorphic representation of GSp(4) over $\mathbb Q$, one can associate a compatible system of Galois representations $\{\rho_p\}_{p \; \mathrm{prime}}$. For $p$ sufficiently large, the deformation theory of the mod-$p$ reduction $\overline \rho_p$ is expected to be unobstructed -- meaning the universal deformation ring is a power series ring. The global obstructions to deforming $\overline \rho_p$ is controlled by certain adjoint Bloch-Kato Selmer groups, which are expected to be trivial for $p$ large enough.

I will talk about some recent results showing that there are no local obstructions to the deformation theory of $\overline \rho_p$ for almost all $p$. This is joint work with M. Broshi, C. Sorensen, and T. Weston.

number theory

Audience: researchers in the topic

( paper )

Comments: Pre-talk

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UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.

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