Related papers: Iwasawa theory and p-adic L-functions over $\mathb…

This paper is lead by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, R of a p-adic analytic group G. For G without any p-torsion element we…

Let X_d be the p-adic analytic space classifying the d-dimensional (semisimple) p-adic Galois representations of the absolute Galois group of Q_p. We show that the crystalline representations are Zarski-dense in many irreducible components…

We consider a model of cyclic time evolution for Kochubei's p-adic realization of the canonical commutation relations (CCR). Connections to Kubota-Leopoldt p-adic zeta-functions and to arithmetic quantum theories such as the Bost-Connes…

The principal aim of this article is to attach and study $p$-adic $L$-functions to cohomological cuspidal automorphic representations $\Pi$ of $\mathrm{GL}(2n)$ over a totally real field $F$ admitting a Shalika model. We use a modular…

We discuss the formalism of Iwasawa theory descent in the setting of the localized K_1-groups of Fukaya and Kato. We then prove interpolation formulas for the `leading terms' of the global Zeta isomorphisms that are associated to certain…

We propose the notion of the {\em crystalline sub-representation functor} defined on $p$-adic representations of the Galois groups of finite extensions of $\Qp$, with certain restrictions in the case of integral representations. By studying…

Let $A$ be an abelian variety defined over a global field $F$ of positive characteristic $p$ and let $\calf/F$ be a $\Z_p^{\N}$-extension, unramified outside a finite set of places of $F$. Assuming that all ramified places are totally…

Let $f_{\mathrm{new}}$ be a classical newform of weight $\geq 2$ and prime to $p$ level. We study the arithmetic of $f_{\mathrm{new}}$ and its unique $p$-stabilisation $f$ when $f_{\mathrm{new}}$ is $p$-irregular, that is, when its Hecke…

The goal of this paper is to illustrate different approaches to understand Euler characteristics in the setting of totally real commutative and non-commutative Iwasawa theory. In addition to this, and in the spirit of Hesselholt and…

In this paper, we propose and explore a new connection in the study of $p$-adic $L$-functions and eigenvarieties. We use it to prove results on the geometry of the cuspidal eigenvariety for $\mathrm{GL}_{2n}$ over a totally real number…

We prove the existence of a new structure on the first Galois cohomology of generic families of symplectic self-dual $p$-adic representations of $G_{\mathbb{Q}_p}$ of rank two (a local sign decomposition): a functorial decomposition into…

This paper completes the construction of $p$-adic $L$-functions for unitary groups. More precisely, in 2006, the last three named authors proposed an approach to constructing such $p$-adic $L$-functions (Part I). Building on more recent…

Let K/Q be a Galois extension of degree n, of Galois group G, and let $\eta\in K^\times$. For all large enough prime p, we define, by use of the Frobenius theorem on group determinants, the family $(\Delta_p^\theta(\eta) \in \F_p)_\theta$…

Let p be an odd prime and let L/k be a Galois extension of number fields whose Galois group is isomorphic to the dihedral group of order 2p. Let S be a finite set of primes of L which is stable under the action of Gal(L/k). The Lichtenbaum…

We define a pro-$p$ Abelian sheaf on a modular curve of a fixed level $N \geq 5$ divisible by a prime number $p \neq 2$. Every $p$-adic representation of $\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ associated to an eigenform is obtained…

Let A be an abelian variety defined over a number field k and let F be a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we compute explicitly the algebraic part of the…

We study an analogue of the Herbrand-Ribet theorem, and its refinement by Mazur and Wiles, in graph theory. For an odd prime number $p$, we let $\mathbb{F}_{p}$ and $\mathbb{Z}_{p}$ denote the finite field with $p$ elements and the ring of…

Let K be a number field. We prove that its ray class group modulo p 2 (resp. 8) if p > 2 (resp. p = 2) characterizes its p-rationality. Then we give two short, very fast PARI Programs (\S \S 3.1, 3.2) testing if K (defined by an irreducible…

We prove the conjectured compatibility of $p$-adic fundamental lines with specializations at motivic points for a wide class of $p$-adic families of $p$-adic Galois representations (for instance, the families which arise from $p$-adic…

Bertolini-Darmon and Mok proved a formula of the second derivative of the two-variable $p$-adic $L$-function of a modular elliptic curve over a totally real field along the Hida family in terms of the image of a global point by some…