On p-ordinary, mod p local Langlands correspondences.

Abstract: To a suitably “nice" automorphic representation we can attach a p-adic representation of the absolute Galois group of a number field. We call a Galois representation arising in this way automorphic. One goal of the Langlands programme is prove various conjectures that classify the image of a correspondence with automorphic Galois representations in the set of all Galois representations. When n = 2 and the number field is the rationals, a correspondence was built from combining mod p and p-adic correspondences with local-global compatibility results. The p-adic correspondence in this case is a representation of GL2(Qp), associated to a local Galois representation, which occurs in the cohomology of the modular curve. In work of Breuil and Herzig a candidate for a more general correspondence for p-ordinary local Galois representations was constructed. In this talk I will discuss joint work of myself and Shu Sasaki in which we construct a purely local framework which should generalise Breuil and Herzig’s mod p results, in particular allowing for the non-generic case. We will examine our construction in a maximally non-split example highlighting the representations that can occur in the graded pieces.

number theory

Audience: researchers in the topic

London number theory seminar

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