Fine Selmer group of Hida deformations over non-commutative $p$-adic Lie extensions

On the Structure of Selmer Groups of Λ-Adic Deformations over p-Adic Lie Extensions

In this paper, we consider the Λ-adic deformations of Galois representations associated to elliptic curves. We prove that the Pontryagin dual of the Selmer group of a Λ-adic deformation over certain p-adic Lie extensions of a number field, that are not necessarily commutative, has no non-zero pseudo-null submodule. We also study the structure of various arithmetic Iwasawa modules associated to ...

Galois Extensions over Commutative and Non-commutative Base

This paper is a written form of a talk. It gives a review of various notions of Galois (and in particular cleft) extensions. Extensions by coalgebras, bialgebras and Hopf algebras (over a commutative base ring) and by corings, bialgebroids and Hopf algebroids (over a non-commutative base algebra) are systematically recalled and compared. In the first version of this paper, the journal version o...

INDUCTIVE CONSTRUCTION OF THE p-ADIC ZETA FUNCTIONS FOR NON-COMMUTATIVE p-EXTENSIONS OF TOTALLY REAL FIELDS WITH EXPONENT p

In this paper, we will construct the p-adic zeta function for a non-commutative p-extension F of a totally real number field F such that the finite part of its Galois group G is a p-group with exponent p. We first calculate the Whitehead groups of the Iwasawa algebra Λ(G) and its canonical Ore localization Λ(G)S by using Oliver-Taylor’s theory on integral logarithms. Then we reduce the main con...

Group Rings over the p-Adic Integers

p-adic L-functions over the false Tate curve extensions

Let f be a primitive modular form of CM type of weight k and level 0(N ). Let p be an odd prime which does not divide N , and for which f is ordinary. Our aim is to padically interpolate suitably normalized versions of the critical values L( f, ρχ, n), where n = 1, 2, . . . , k − 1, ρ is a fixed self-dual Artin representation of M∞ defined by (1·1) below, and χ runs over the irreducible Artin r...