155,591 research outputs found
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
Bloch and Kato's exponential map: three explicit formulas
The purpose of this article is to give formulas for Bloch-Kato's exponential
map and its dual for an absolutely crystalline p-adic representation V, in
terms of the (phi,Gamma)-module associated to that representation. As a
corollary of these computations, we can give a very simple (and slightly
improved) description of Perrin-Riou's exponential map (which interpolates
Bloch-Kato's exponentials for V(k)). This new description directly implies
Perrin-Riou's reciprocity formula.Comment: 22 pages, in englis
On Euler systems of rank and their Kolyvagin systems
In this paper we set up a general Kolyvagin system machinery for Euler
systems of rank r (in the sense of Perrin-Riou) associated to a large class of
Galois representations, building on our previous work on Kolyvagin systems of
Rubin-Stark units and generalizing the results of Kato, Rubin and Perrin-Riou.
Our machinery produces a bound on the size of the classical Selmer group
attached to a Galoys representation T (that satisfies certain technical
hypotheses) in terms of a certain r \times r determinant; a bound which
remarkably goes hand in hand with Bloch-Kato conjectures. At the end, we
present an application based on a conjecture of Perrin-Riou on p-adic
L-functions, which lends further evidence to Bloch-Kato conjectures.Comment: 43 pages, to appear in Indiana U. Math. Journal. May differ from the
final versio
Microscopic dynamics of thin hard rods
Based on the collision rules for hard needles we derive a hydrodynamic
equation that determines the coupled translational and rotational dynamics of a
tagged thin rod in an ensemble of identical rods. Specifically, based on a
Pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig
projection formalism is used to derive a continued fraction representation for
the correlation function of the tagged particle's density, specifying its
position and orientation. Truncation of the continued fraction gives rise to a
generalised Enskog equation, which can be compared to the phenomenological
Perrin equation for anisotropic diffusion. Only for sufficiently large density
do we observe anisotropic diffusion, as indicated by an anisotropic mean square
displacement, growing linearly with time. For lower densities, the Perrin
equation is shown to be an insufficient hydrodynamic description for hard
needles interacting via binary collisions. We compare our results to
simulations and find excellent quantitative agreement for low densities and
qualtitative agreement for higher densities.Comment: 21 pages, 6 figures, v2: clarifications and improved readabilit
The m−Order Linear Recursive Quaternions
This study considers the m−order linear recursive sequences yielding some well-known
sequences (such as the Fibonacci, Lucas, Pell, Jacobsthal, Padovan, and Perrin sequences). Also,
the Binet-like formulas and generating functions of the m−order linear recursive sequences have
been derived. Then, we define the m−order linear recursive quaternions, and give the Binet-like
formulas and generating functions for them
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