30 research outputs found
Links between generalized Montr\'eal-functors
Let be the ring of integers in a finite extension and
be the -points of a
-split reductive group defined over
with connected centre and split Borel . We show that
Breuil's pseudocompact -module attached
to a smooth -torsion representation of is
isomorphic to the pseudocompact completion of the basechange
to Fontaine's
ring (via a Whittaker functional ) of the \'etale hull of
defined by Schneider and Vigneras. Moreover, we construct a -equivariant map
from the Pontryagin dual to the global sections
of the -equivariant sheaf on attached to a
noncommutative multivariable version of
Breuil's whenever comes as the restriction to of
a smooth, admissible representation of of finite length.Comment: 50 pp, revise
On twists of modules over non-commutative Iwasawa algebras
It is well known that, for any finitely generated torsion module M over the
Iwasawa algebra Z_p [[{\Gamma} ]], where {\Gamma} is isomorphic to Z_p, there
exists a continuous p-adic character {\rho} of {\Gamma} such that, for every
open subgroup U of {\Gamma}, the group of U-coinvariants M({\rho})_U is finite;
here M( {\rho}) denotes the twist of M by {\rho}. This twisting lemma was
already applied to study various arithmetic properties of Selmer groups and
Galois cohomologies over a cyclotomic tower by Greenberg and Perrin-Riou. We
prove a non commutative generalization of this twisting lemma replacing torsion
modules over Z_p [[ {\Gamma} ]] by certain torsion modules over Z_p [[G]] with
more general p-adic Lie group G.Comment: submitte
(\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