195 research outputs found
Locally analytic vectors of some crystabelian representations of GL_2(Qp)
For V a 2-dimensional p-adic representation of G_Qp, we denote by B(V) the
admissible unitary representation of GL_2(Qp) attached to V under the p-adic
local Langlands correspondence of GL_2(Qp) initiated by Breuil. In this
article, building on the works of Berger-Breuil and Colmez, we determine the
locally analytic vectors B(V)an of B(V) when V is irreducible, crystabelian and
Frobenius semi-simple with Hodge-Tate weights (0,k-1) for some integer k>=2;
this proves a conjecture of Breuil. Using this result, we verify Emerton's
conjecture that dim Ref^{\eta\otimes\psi}(V)=dim Exp^{\eta|\cdot|\otimes
x\psi}(B(V)an\otimes(x|\cdot|\circ\det)) for those V which are irreducible,
crystabelian and not exceptional.Comment: Refereed version. Title is changed. Minor changes in the conten
(\phi,\Gamma)-modules over noncommutative overconvergent and Robba rings
We construct noncommutative multidimensional versions of overconvergent power
series rings and Robba rings. We show that the category of \'etale
-modules over certain completions of these rings are
equivalent to the category of \'etale -modules over the
corresponding classical overconvergent, resp. Robba rings (hence also to the
category of -adic Galois representations of ). Moreover, in
the case of Robba rings, the assumption of \'etaleness is not necessary, so
there exists a notion of trianguline objects in this sense.Comment: 41 pages, revise
Triangulable \CO_F-analytic -modules of rank 2
The theory of -modules is a generalization of Fontaine's
theory of -modules, which classifies -representations on
\CO_F-modules and -vector spaces for any finite extension of \BQ_p.
In this paper following Colmez's method we classify triangulable
\CO_F-analytic -modules of rank 2. In this process we
establish two kinds of cohomology theories for \CO_F-analytic
-modules. Using them we show that, if is an
\CO_F-analytic -module such that
i.e. where is the Galois
representation attached to , then any overconvergent extension of the
trivial representation of by is \CO_F-analytic. In particular,
contrarily to the case of F=\BQ_p, there are representations of that
are not overconvergent.Comment: 35 page
Exactness of the reduction on \'etale modules
We prove the exactness of the reduction map from \'etale
-modules over completed localized group rings of compact open
subgroups of unipotent -adic algebraic groups to usual \'etale
-modules over Fontaine's ring. This reduction map is a component
of a functor from smooth -power torsion representations of -adic
reductive groups (or more generally of Borel subgroups of these) to
-modules. Therefore this gives evidence for this functor---which
is intended as some kind of -adic Langlands correspondence for reductive
groups---to be exact. We also show that the corresponding higher
\Tor-functors vanish. Moreover, we give the example of the Steinberg
representation as an illustration and show that it is acyclic for this functor
to -modules whenever our reductive group is
\GL_{d+1}(\mathbb{Q}_p) for some .Comment: 18 pages; some typos corrected and proof of Lemma 1 rewritten, to
appear in Journal of Algebr
LOCALLY ANALYTIC VECTORS AND OVERCONVERGENT (phi, tau)-MODULES
Let p be a prime, let K be a complete discrete valuation field of characteristic 0 with a perfect residue field of characteristic p, and let G(K) be the Galois group. Let pi be a fixed uniformizer of K, let K-infinity be the extension by adjoining to K a system of compatible p(n) th roots of pi for all n, and let L be the Galois closure of K-infinity. Using these field extensions, Caruso constructs the (phi, tau)-modules, which classify p-adic Galois representations of G(K). In this paper, we study locally analytic vectors in some period rings with respect to the p -adic Lie group Gal(L/K), in the spirit of the work by Berger and Colmez. Using these locally analytic vectors, and using the classical overconvergent (phi, Gamma)-modules, we can establish the overconvergence property of the (phi, tau)-modules.Peer reviewe
The p-adic L-functions of Evil Eisenstein Series
We compute the -adic -functions of evil Eisenstein series, showing that
they factor as products of two Kubota--Leopoldt -adic -functions times a
logarithmic term. This proves in particular a conjecture of Glenn Stevens.Comment: 49 page
Filtered modules corresponding to potentially semi-stable representations
We classify the filtered modules with coefficients corresponding to
two-dimensional potentially semi-stable -adic representations of the
absolute Galois groups of -adic fields under the assumptions that is odd
and the coefficients are large enough.Comment: 19 page
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