29 research outputs found
Smoothness and Classicality on eigenvarieties
Let p be a prime number and f an overconvergent p-adic automorphic form on a
definite unitary group which is split at p. Assume that f is of "classical
weight" and that its Galois representation is crystalline at places dividing p,
then f is conjectured to be a classical automorphic form. We prove new cases of
this conjecture in arbitrary dimension by making crucial use of the "patched
eigenvariety"
A local model for the trianguline variety and applications
We describe the completed local rings of the trianguline variety at certain
points of integral weights in terms of completed local rings of algebraic
varieties related to Grothendieck's simultaneous resolution of singularities.
We derive several local consequences at these points for the trianguline
variety: local irreducibility, description of all local companion points in the
crystalline case, combinatorial description of the completed local rings of the
fiber over the weight map, etc. Combined with the patched Hecke eigenvariety
(under the usual Taylor-Wiles assumptions), these results in turn have several
global consequences: classicality of crystalline strictly dominant points on
global Hecke eigenvarieties, existence of all expected companion constituents
in the completed cohomology, existence of singularities on global Hecke
eigenvarieties
On arithmetic families of filtered φ-modules and crystalline representations
We consider stacks of filtered phi-modules over rigid analytic and adic spaces. We show that these modules parametrize p-adic Galois representations of the absolute Galois group of a p-adic field with varying coefficients over an open substack containing all classical points. Further we study a period morphism (defined by Pappas and Rapoport) from a stack parametrizing integral data and determine the image of this morphism
An introduction to the categorical p-adic Langlands program
We give an introduction to the "categorical" approach to the p-adic Langlands
program, in both the "Banach" and "analytic" settings.Comment: 210 pages. Preliminary version; comments and corrections would be
very welcome, particularly before the end of November when we need to submit
this for publicatio