Deformations of polarized automorphic Galois representations and adjoint Selmer groups

By P. Allen. 2014

50 citations recorded by the source corpus.

We prove the vanishing of the geometric Bloch-Kato Selmer group for the adjoint representation of a Galois representation associated to regular algebraic polarized cuspidal automorphic representations under an assumption on the residual image. Using this, we deduce that the localization and completion of a certain universal deformation ring for the residual representation at the characteristic zero point induced from the automorphic representation is formally smooth of the correct dimension. We do this by employing the Taylor-Wiles-Kisin patching method together with Kisin's technique of analyzing the generic fibre of universal deformation rings. Along the way we give a characterization of smooth closed points on the generic fibre of Kisin's potentially semistable local deformation rings in terms of their Weil-Deligne representations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a8843fcd4ec9eff2ee5fdb348c2ef9c2f3a428b1

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In Geometry and Topology

1. Netan Dogra
2. Jennifer S. Balakrishnan

In Mathematical Physics

1. Jennifer S. Balakrishnan
2. Netan Dogra

Citations in the corpus

• Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties (2017, background): “Then we have that for all k < 2g − 1, r k ∈ H(X,D[1]).”