61,558 research outputs found
Residual irreducibility of compatible systems
We show that if is a compatible system of absolutely
irreducible Galois representations of a number field then the residual
representation is absolutely irreducible for in
a density 1 set of primes. The key technical result is the following theorem:
the image of is an open subgroup of a hyperspecial maximal
compact subgroup of its Zariski closure with bounded index (as varies).
This result combines a theorem of Larsen on the semi-simple part of the image
with an analogous result for the central torus that was recently proved by
Barnet-Lamb, Gee, Geraghty, and Taylor, and for which we give a new proof.Comment: 11 page
On weakly maximal representations of surface groups
We introduce and study a new class of representations of surface groups into
Lie groups of Hermitian type, called {\em weakly maximal} representations. We
prove that weakly maximal representations are discrete and injective and we
describe the structure of the Zariski closure of their image. Furthermore we
prove that the set of weakly maximal representations is a closed subset of the
representation variety and describe its relation to other geometrically
significant subsets of the representation variety.Comment: In this version the paper has been split in two parts. The part that
has been removed appears now as http://arxiv.org/abs/1601.02232. The current
version of the paper will appear in the Journal of Differential Geometr
Curtis homomorphisms and the integral Bernstein center for GL_n
We describe two conjectures, one strictly stronger than the other, that give
descriptions of the integral Bernstein center for GL_n(F) (that is, the center
of the category of smooth W(k)[GL_n(F)]-modules, for F a p-adic field and k an
algebraically closed field of characteristic l different from p) in terms of
Galois theory. Moreover, we show that the weak version of the conjecture (for m
at most n) implies the strong version of the conjecture. In a companion paper
[HM] we show that the strong conjecture for n-1 implies the weak conjecture for
n; thus the two papers together give an inductive proof of both conjectures.
The upshot is a description of the integral Bernstein center for GL_n in purely
Galois-theoretic terms; previous work of the author shows that such a
description implies the conjectural "local Langlands correspondence in
families" of Emerton and the author.Comment: Final accepted version. 36 pages. Note that the published version of
Helm-Moss, "Converse theorems and the local Langlands correspondence in
families" references an earlier version of this paper, and the section
numbering has changed; in particular sections 9,10, and 11 of the referenced
version correspond to sections 8,9, and 10 of the current version,
respectivel
Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras
-algebraic Weyl quantization is extended by allowing also degenerate
pre-symplectic forms for the Weyl relations with infinitely many degrees of
freedom, and by starting out from enlarged classical Poisson algebras. A
powerful tool is found in the construction of Poisson algebras and
non-commutative twisted Banach--algebras on the stage of measures on the not
locally compact test function space. Already within this frame strict
deformation quantization is obtained, but in terms of Banach--algebras
instead of -algebras. Fourier transformation and representation theory of
the measure Banach--algebras are combined with the theory of continuous
projective group representations to arrive at the genuine -algebraic
strict deformation quantization in the sense of Rieffel and Landsman. Weyl
quantization is recognized to depend in the first step functorially on the (in
general) infinite dimensional, pre-symplectic test function space; but in the
second step one has to select a family of representations, indexed by the
deformation parameter . The latter ambiguity is in the present
investigation connected with the choice of a folium of states, a structure,
which does not necessarily require a Hilbert space representation.Comment: This is a contribution to the Special Issue on Deformation
Quantization, published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
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