Related papers: On anticyclotomic Euler and Kolyvagin systems

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…

We study this subject by first proving that the p-primary subgroup of the classical Selmer group for an elliptic curve with good, ordinary reduction at a prime p has a very simple and elegant description which involves just the Galois…

We construct an Euler system associated to regular algebraic, essentially conjugate self-dual cuspidal automorphic representations of GL(3) over imaginary quadratic fields, using the cohomology of Shimura varieties for GU(2, 1).

Let $f$ be a newform of even weight at least $4$, level $N$ and trivial character. Let $p\nmid N$ be an odd prime number that is ordinary for $f$ and let $K$ be an imaginary quadratic field satisfying a generalized Heegner hypothesis…

Let $p$ be an odd prime. We prove the cyclotomic Iwasawa Main Conjecture of K.Kato for the motive attached to an eigencuspform $f\in S_{k}(\Gamma_{0}(N))$ with arbitrary reduction type at $p$ under mild assumptions on the residual Galois…

We investigate fine Selmer groups for elliptic curves and for Galois representations over a number field. More specifically, we discuss Conjecture A, which states that the fine Selmer group of an elliptic curve over the cyclotomic extension…

We construct a global geometric model for complex analytic equivariant elliptic cohomology for all compact Lie groups. Cocycles are specified by functions on the space of fields of the two-dimensional sigma model with background gauge…

In this paper, we relate three objects. The first is a particular value of a cup product in the cohomology of the Galois group of the maximal unramified outside p extension of a cyclotomic field containing the pth roots of unity. The second…

We deduce the cyclotomic Iwasawa main conjecture for Hilbert modular cuspforms with complex multiplication from the multivariable main conjecture for CM number fields. To this end, we study in detail the behaviour of the $p$-adic…

We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor--Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the…

We develop local cohomology techniques to study the finite slope part of the coherent cohomology of Shimura varieties. The local cohomology groups we consider are a generalization of overconvergent modular forms, and they are defined by…

We prove a formula (analogous to that of Kida in classical Iwasawa theory and generalizing that of Hachimori-Matsuno for elliptic curves) giving the analytic and algebraic p-adic Iwasawa invariants of a modular eigenform over an abelian…

The main conjecture of Iwasawa theory is a conjecture on the relation between a Selmer group and a conjectural $p$-adic $L$-function. This conjectural $p$-adic $L$-function is expected to satisfy a conjectural functional equation in a…

As a natural generalization of the notion of `higher rank Euler system', we develop a theory of `higher special elements' in the exterior power biduals of the Galois cohomology of $p$-adic representations. We show, in particular, that such…

In this paper we explain how to attach to a family of $p$-adic representations of a product of Galois groups an overconvergent family of multivariable $(\varphi,\Gamma)$-modules, generalizing results from Pal-Zabradi and…

This paper is a sequel to our earlier paper "Wach modules and Iwasawa theory for modular forms" (arXiv: 0912.1263), where we defined a family of Coleman maps for a crystalline representation of the Galois group of Qp with nonnegative…

For a prime number p and a number field k, we first study certain etale cohomology groups with coefficients associated to a p-adic Artin representation of its Galois group, where we twist the coefficients using a modified Tate twist with a…

In this article, we set up a strategy to prove one divisibility towards the main Iwasawa conjecture for the Selmer groups attached to the twisted adjoint modular Galois representations associated to Hida families. This conjecture asserts…

We describe a Kolyvagin system-theoretic refinement of Gross--Zagier formula by comparing Heegner point Kolyvagin systems with Kurihara numbers when the root number of a rational elliptic curve $E$ over an imaginary quadratic field $K$ is…

This is the final version of a book about p-adic families of Galois representations, Selmer groups, eigenvarieties and Arthur's conjectures