The image of Colmez’s Montreal functor

By Vytautas Paškūnas. Publications mathématiques (Bures-sur-Yvette), 2010

159 citations recorded by the source corpus.

AbstractWe prove a conjecture of Colmez concerning the reduction modulo p of invariant lattices in irreducible admissible unitary p-adic Banach space representations of GL2(Q p) with p≥5. This enables us to restate nicely the p-adic local Langlands correspondence for GL2(Q p) and deduce a conjecture of Breuil on irreducible admissible unitary completions of locally algebraic representations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/670606c6e9f5e372ea595287aee0bc8e430d6722

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Citations in the corpus

On the Breuil–Mézard conjecture (2012, methodology): “We use the results of [53] instead of the global input.”
Lattices in the cohomology of Shimura curves (2013, background): “[20,39]) is one of the most important developments in the Langlands program in recent years, and the natural and definitive nature of the results is extremely suggestive of there being a similar correspondence for GLn(K ), where n is an arbitrary natural number and K an arbitrary finite extension of”
The p-adic local Langlands correspondence for GL_2(Q_p) (2013, methodology): “However, the fact that E is commutative is a very useful piece of information, and, when π is either supersingular or generic principal series, in a forthcoming paper [55] we will extend the results of [54] to the cases when p = 2 and p = 3.”
On the p-adic cohomology of the Lubin-Tate tower (2015, methodology): “The goal of this paper is to provide further evidence for the existence of a p-adic local Langlands correspondence, as was first envisioned by Breuil, [2], and established for GL2(Qp) by Colmez, [12], Paskunas, [25], and others.”