1.1. The local-global compatibility conjecture. Fix a prime p, as well as a finite extension E of Qp. If K is an open subgroup of GL2(Ẑ) (referred to as a “tame level”), then one can define a certain… (More)

This note summarizes the theory of p-adically completed cohomology. This construction was first introduced in paper [4] (although insufficient attention was given there to the integral aspects of the… (More)

Hereditary multiple exostoses (HME), the most frequent of all skeletal dysplasias, is an autosomal dominant disorder characterized by the presence of multiple exostoses localized mainly at the end of… (More)

Let ρ̄ : GQ → GL2(k) be an absolutely irreducible modular Galois representation over a finite field k of characteristic p. Assume further that ρ̄ is p-ordinary and p-distinguished in the sense that… (More)

Acknowledgements I thank my supervisor, Karen Smith, for her excellent guidance during the years of my doctoral studies. Without her support, expertise and, most importantly, encouragement this… (More)

In the first half of the paper we introduce the notion of the universal unitary completion of a continuous representation of a p-adic reductive group on a locally convex p-adic vector space, and… (More)

The goal of this paper, which is a sequel to [10], is to extend the functors of ordinary parts introduced in that paper to certain δ-functors. On the one hand, the δ-functors that we construct are… (More)

This paper deals with two subjects and their interaction. The first is the problem of spanning spaces of modular forms by theta series. The second is the commutative algebraic properties of Hecke… (More)

1.1. The local Langlands correspondence for GLn in p-adic families. Let p and ` be distinct primes, and let E be a local field of residue characteristic `. If A is a complete local domain of… (More)