Seminario de Teoría de Números (Martes 08 de abril - 14:30)

Title: Zig-zag holds for Galois representations

SPEAKER: Eknath Ghate (Tata Institute of Fundamental Research)

DATE & TIME: Martes 08 de abril - 14:30

VENUE: Aula 420, 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-Mézard, Guerberoff-Park, and most  
recently, Chitrao-Ghate, all in the semi-stable case.