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

By M. Emerton. 2006

236 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/465139f45836bcd3b63aa6e54d47eb4620c12732

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

The asymptotic growth of torsion homology for arithmetic groups (2010, background): “[13, 28, 38] and an unpublished manuscript by Clozel and Belabas where they make precise computations for SL2 over an imaginary quadratic field).”
Overconvergent algebraic automorphic forms (2009, methodology): “This theory, which does not require G(F ⊗ R) to be compact modulo centre but at present requires G(Fp) to be quasi-split, is in a sense opposite to the approach followed here: for each i ≥ 0, Emerton builds a locally analytic representation H̃iFp−la of the whole ofG(Fp) which “sees” all automorphic ”
ORDINARY PARTS OF ADMISSIBLE REPRESENTATIONS OF p-ADIC REDUCTIVE GROUPS I. DEFINITION AND FIRST PROPERTIES (2007, background): “They also have important global applications: when applied in the context of the p-adically completed cohomology spaces introduced in [7], they provide a representation theoretic approach to Hida's theory of (nearly) ordinary parts of cohomology [11] [12] [13].”
Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms (2007, background): “(Note that the results of [4] are stated in the adèlic language.”
The emerging p-adic Langlands programme (2011, background): “Strangely, the terminology “p-adic Langlands correspondence/programme” started to spread (at least in the author’s memory) only shortly after preprints of [6], [7], [8], [9], [14], [19], [24], [53], [59], [60], [61], [70] were available (that is, around 2004), although of course p-adic consideration”
A Local-Global Compatibility Conjecture in the p-adic Langlands Programme for GL 2/Q (2006, unknown): “We recall some constructions from [33].”
A torsion Jacquet--Langlands correspondence (2012, background): “What might one expect be the ultimate version of an integral Jacquet–Langlands theorem for homology to be? A plausible candidate for a formulation (completed at a prime p) would use the notion of completed cohomology: Consider the following completed homology groups (see [32, 19])”
Jacquet modules of locally analytic representations of p-adic reductive groups I. Construction and first properties (2006, methodology): “The Jacquet module of an admissible locally analytic G-representation V , while certainly essentially admissible, need not be an admissible locally analytic M -representation (as the examples of [9] show).”