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On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms

- M. Emerton
- Mathematics
- 31 January 2006

The goal of this paper is to illustrate how the techniques of locally analytic p-adic representation theory (as developed in [28, 29, 30, 31] and [13, 14, 17]; see also [16] for a short summary of… Expand

The Riemann-Hilbert correspondence for unit F-crystals

- M. Emerton, M. Kisin
- Mathematics
- 2004

として(独立に)定式化した. ここにDX はX上の微分作用素のなす環の層であり, 前者の 圏の対象はX 上の線形偏微分方程式系を起源を持つ. 一方で構成可能層とは局所系の一般 化であり, 後者の圏の対象は位相幾何学的である. この圏同値はコホモロジー理論の観点か ら重要な意味をもつ. Db rh(DX)にはGrothendieckの6つの演算 f∗, f∗, f!, f !, ⊗L, Homが… Expand

A Local-Global Compatibility Conjecture in the p-adic Langlands Programme for GL 2/Q

- M. Emerton
- Mathematics
- 2006

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… Expand

Variation of Iwasawa invariants in Hida families

- M. Emerton, R. Pollack, T. Weston
- Mathematics
- 27 April 2004

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

Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms

- Frank Calegari, M. Emerton
- Mathematics
- 4 April 2007

Let Goo be a semisimple real Lie group with unitary dual Goo- We produce new upper bounds for the multiplicities with which representations ^ e of cohomological type appear in certain spaces of cusp… Expand

Locally analytic vectors in representations of locally p-adic analytic groups

- M. Emerton
- Mathematics
- 7 May 2004

This paper develops various foundational results in the locally analytic representation theory of p-adic groups. In particular, we define the functor ``pass to locally analytic vectors'', which… Expand

Patching and the p-adic local Langlands correspondence

- A. Caraiani, M. Emerton, T. Gee, D. Geraghty, Vytautas Paškūnas, S. Shin
- Mathematics
- 2 October 2013

We use the patching method of Taylor--Wiles and Kisin to construct a candidate for the p-adic local Langlands correspondence for GL_n(F), F a finite extension of Q_p. We use our construction to prove… Expand

ORDINARY PARTS OF ADMISSIBLE REPRESENTATIONS OF p-ADIC REDUCTIVE GROUPS II. DERIVED FUNCTORS

- M. Emerton
- Mathematics
- 2010

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… Expand

Lattices in the cohomology of Shimura curves

- M. Emerton, T. Gee, David Savitt
- Mathematics
- 7 May 2013

We prove the main conjectures of Breuil (J Reine Angew Math, 2012) (including a generalisation from the principal series to the cuspidal case) and Dembélé (J Reine Angew Math, 2012), subject to a… Expand

The local Langlands correspondence for GL_n in families

- M. Emerton, David Helm
- Mathematics
- 2 April 2011

Let E be a nonarchimedean local field with residue characteristic l, and suppose we have an n-dimensional representation of the absolute Galois group G_E of E over a reduced complete Noetherian local… Expand

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