Related papers: Bipartite Euler Systems for certain Galois Represe…

In this note we show how the main conjecture of the Iwasawa theory over Q has a natural place in the context of the Galois representation of the Galois group $Gal(\bar Q/Q)$ on the etale pro-p fundamental group of the projective line minus…

Let $K$ be an imaginary quadratic field where $p$ splits, $p\geq5$ a prime number and $f$ an eigen-newform of even weight and level $N>3$ that is coprime to $p$. Under the Heegner hypothesis, Kobayashi--Ota showed that one inclusion of the…

Let $E/\mathbf{Q}$ be an elliptic curve and $p\geq 3$ be a prime. We prove the $p$-converse theorems for elliptic curves of potentially good ordinary reduction at Eisenstein primes (i.e., such that the residual representation $E[p]$ is…

Euler systems are certain compatible families of cohomology classes, which play a key role in studying the arithmetic of Galois representations. We briefly survey the known Euler systems, and recall a standard conjecture of Perrin-Riou…

We formulate for function fields an analog of Serre's conjecture on the modularity of 2-dimensional irreducible mod l representations of the absolute Galois group of Q: our analog is not restricted to 2-dimensional represntations. While the…

In this article, we study the Iwasawa theory for cuspidal automorphic representations of $\mathrm{GL}(n)\times\mathrm{GL}(n+1)$ over CM fields along anticyclotomic directions, in the framework of the Gan--Gross--Prasad conjecture for…

Let p be a prime number which is split in an imaginary quadratic field k. Let \mathfrak{p} be a place of k above p. Let k_\infty be the unique Z_p-extension of k which unramified outside of \mathfrak{p}, and let K_\intfy be a finite…

Let $p\geq5$ be a prime number and let $K$ be an imaginary quadratic field where $p$ is unramified. Under mild technical assumptions, in this paper we prove the non-existence of non-trivial finite $\Lambda$-submodules of Pontryagin duals of…

Let p be an odd prime. Suppose that E is a modular elliptic curve/Q with good ordinary reduction at p. Let Q_{oo} denote the cyclotomic Z_p-extension of Q. It is conjectured that Sel_E(Q_{oo}) is a cotorsion Lambda-module and that its…

In this paper we prove that the p-adic L-function that interpolates the Rankin-Selberg product of a general modular form and a CM form of higher weight divides the characteristic ideal of the corresponding Selmer group. This is one…

Given a pair of modular forms with complex multiplication by distinct imaginary quadratic fields, the four dimensional Galois representation associated to their Rankin--Selberg convolution is induced from a character over an imaginary…

We prove an Equivariant Main Conjecture in Iwasawa Theory along any rank one, sign-normalized Drinfeld modular, split at infinity Iwasawa tower of a general function field of characteristic p, for the Iwasawa modules recently considered by…

Let $A$ be an ordinary elliptic curve over a global function field $K$ of characteristic $p$, assumed semistable at every place, and let $L/K$ be a $\mathbb{Z}_p^d$-extension ramified only at finitely many places where $A$ has ordinary…

The goal of this article is two-fold: First, to prove a (two-variable) main conjecture for a CM field $F$ without assuming the $p$-ordinary hypothesis of Katz, making use of what we call the Rubin-Stark $\mathcal{L}$-restricted Kolyvagin…

Let $\rho$ be a conjugate-symplectic, geometric representation of the Galois group of a CM field. Under the assumption that $\rho$ is automorphic, even-dimensional, and of minimal regular Hodge--Tate type, we construct an Euler system for…

Darmon's conjecture on a relation between cyclotomic units over real quadratic fields and certain algebraic regulators was recently solved by Mazur and Rubin by using their theory of Kolyvagin systems. In this paper, we formulate a…

Let $p$ be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for every admissible one-dimensional $p$-adic Lie extension whose Galois group has an abelian Sylow $p$-subgroup.…

We prove the existence of Euler systems for adjoint modular Galois representations using deformations of Galois representations coming from Hilbert modular forms and relate them to $p$-adic $L$-functions under a conjectural formula for the…

In this paper we study a new conjecture concerning Kato's Euler system of zeta elements for elliptic curves $E$ over $\mathbb{Q}$. This conjecture, which we refer to as the `Generalized Perrin-Riou Conjecture', predicts a precise congruence…

Our main result in this article is a proof (under mild technical assumptions) of an analogue for $p$-adic Galois representations attached to a newform $f$ of even weight $k\geq4$ of Kolyvagin's conjecture on the $p$-indivisibility of…