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On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms
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 ofExpand
The Riemann-Hilbert correspondence for unit F-crystals
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
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 certainExpand
Variation of Iwasawa invariants in Hida families
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 theExpand
Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms
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 cuspExpand
Locally analytic vectors in representations of locally p-adic analytic groups
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'', whichExpand
Patching and the p-adic local Langlands correspondence
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 proveExpand
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 areExpand
Lattices in the cohomology of Shimura curves
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 aExpand
The local Langlands correspondence for GL_n in families
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 localExpand