Number Theory Seminar
Zig-zag holds for Galois representations
Speaker: Eknath Ghate (Tata Institute of Fundamental Research)Date: Tuesday, 08 April 2025 - 14:30Place: Aula 420, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
The zig-zag conjecture says that the mod p reductions of crystalline 2-dimensional p-adic Galois representations of exceptional weights with respect to half-integral slopes up to (p-1)/2 vary through a sequence of irreducible and reducible representations. We will give a sketch of our recent proof of this conjecture. The proof uses the _reverse_ of a limiting argument due to Chitrao-Ghate in the rigid-analytic blow-up space of trianguline representations to reduce the proof to works of Breuil-M\'ezard, Guerberoff-Park, and most recently, Chitrao-Ghate, all in the semi-stable case.
