Related papers: Congruences between abelian pseudomeasures, II

In this article, we construct zeta morphisms for the universal deformations of odd absolutely irreducible two dimensional mod p Galois representations satisfying some mild assumptions, and prove that our zeta morphisms interpolate Kato's…

In this paper, we study the Iwasawa theory of a motive whose Hodge-Tate weights are $0$ or $1$ (thence in practice, of a motive associated to an abelian variety) at a non-ordinary prime, over the cyclotomic tower of a number field that is…

We describe an explicit `higher rank' Iwasawa theory for zeta elements associated to the multiplicative group over abelian extensions of general number fields. We then show that this theory leads to a concrete new strategy for proving…

We use logarithmic {\ell}-class groups to take a new view on Greenberg's conjecture about Iwasawa {\ell}-invariants of a totally real number field K. By the way we recall and complete some classical results. Under Leopoldt's conjecture, we…

Let f be a cuspidal newform with complex multiplication (CM) and let p be an odd prime at which f is non-ordinary. We construct admissible p-adic L-functions for the symmetric powers of f, thus verifying general conjectures of Dabrowski and…

Let $p>2$ be a prime. Under mild assumptions, we prove the Iwasawa main conjecture of Kato, for modular forms with general weight and conductor prime to $p$.

In this paper and a forthcoming joint one with Y. Hachimori we study Iwasawa modules over an infinite Galois extension K of a number field k whose Galois group G=G(K/k) is isomorphic to the semidirect product of two copies of the p-adic…

The purpose of this paper is to prove the equality between the algebraic Iwasawa $\lambda$-invariant and the analytic Iwasawa $\lambda$-invariant for a Hilbert cusp form of parallel weight $2$ at an ordinary prime $p$ when the associated…

The main conjectures of Iwasawa theory provide the only general method known at present for studying the mysterious relationship between purely arithmetic problems and the special values of complex L-functions, typified by the conjecture of…

In this paper, we generalize the Quillen-Lichtenbaum Conjecture relating special values of Dedekind zeta functions to algebraic $\mathrm{K}$-groups. The former has been settled by Rost-Voevodsky up to the Iwasawa Main Conjecture. Our…

Let $E$ be an elliptic curve defined over $\mathbb{Q}$ of conductor $N$, $p$ an odd prime of good ordinary reduction such that $E[p]$ is an irreducible Galois module, and $K$ an imaginary quadratic field with all primes dividing $Np$ split.…

Let $K$ be a finite unramified extension of $\Qp$ and let $V$ be a crystalline representation of $\mathrm{Gal}(\Qpbar/K)$. In this article, we give a proof of the $C_{\mathrm{EP}}(L,V)$ conjecture for $L \subset \Qp^{\mathrm{ab}}$ as well…

We study a natural question in the Iwasawa theory of algebraic curves of genus $>1$. Fix a prime number $p$. Let $X$ be a smooth, projective, geometrically irreducible curve defined over a number field $K$ of genus $g>1$, such that the…

We establish the Iwasawa main conjecture for semi-stable abelian varieties over a function field of characteristic $p$ under certain restrictive assumptions. Namely we consider $p$-torsion free $p$-adic Lie extensions of the base field…

For a prime number $p$ and a number field $k$, let $\tilde{k}$ be the compositum of all $\mathbb{Z}_p$-extensions of $k$. Greenberg's Generalized Conjecture (GGC) claims the pseudo-nullity of the unramified Iwasawa module $X(\tilde{k})$ of…

In this paper, for a CM abelian extension $K/k$ of number fields, we propose a conjecture which describes completely the Fitting ideal of the minus part of the Pontryagin dual of the $T$-ray class group of $K$ for a set $T$ of primes as a…

The Iwasawa theory of CM fields has traditionally concerned Iwasawa modules that are abelian pro-p Galois groups with ramification allowed at a maximal set of primes over p such that the module is torsion. A main conjecture for such an…

Let $K$ be a CM field and $K^+$ be the maximal totally real subfield of $K$. Assume that the primes above $p$ in $K^+$ split in $K$. Let $S$ be a set containing exactly half of the prime ideals in $K$ above $p$. We show, assuming Leopoldt's…

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…

Let p be an odd prime satisfying Vandiver's conjecture. We consider two objects, the Galois group X of the maximal unramified abelian pro-p extension of the compositum of all Z_p-extensions of the pth cyclotomic field and the Galois group G…