The geometric Breuil-M\'ezard conjecture for two-dimensional potentially Barsotti-Tate Galois representations

Ana Caraiani; David Savitt; Matthew Emerton; Toby Gee

The geometric Breuil-M\'ezard conjecture for two-dimensional potentially Barsotti-Tate Galois representations

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arxiv 2207.05235 v2 pith:F32RIW4C submitted 2022-07-12 math.NT

The geometric Breuil-M\'ezard conjecture for two-dimensional potentially Barsotti-Tate Galois representations

Ana Caraiani , Matthew Emerton , Toby Gee , David Savitt This is my paper

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keywords conjecturerepresentationsbarsotti-tatebreuil-mezardgaloispotentiallytwo-dimensional

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We establish a geometrisation of the Breuil-M\'ezard conjecture for potentially Barsotti-Tate representations, as well as of the weight part of Serre's conjecture, for moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field.

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Non-admissibility of some universal supersingular representations
math.NT 2026-05 unverdicted novelty 5.0

For n greater than or equal to 3 and sufficiently generic weights, the universal supersingular representation of GL_n(k) is non-admissible and of infinite length.