Related papers: Wach modules and Iwasawa theory for modular forms

The eigencurve is a powerful tool introduced by Coleman and Mazur to study $p$-adic families of overconvergent modular forms. In this article, we introduce an analogous set of tools for understanding families of "overconvergent" $p$-adic…

Let $K$ be an imaginary quadratic field and $p$ a prime split in $K$. In this paper we construct an anticyclotomic Euler system for the adjoint representation attached to elliptic modular forms base changed to $K$. We also relate our Euler…

We prove the Bloch-Kato conjecture for critical values of Asai L-functions of p-ordinary Hilbert modular forms over quadratic fields (with p split); and one inclusion in the Iwasawa main conjecture for these L-functions (up to a power of…

Let K be a complete discretely valued field of mixed characteristics (0, p) with perfect residue field. One of the central objects of study in p-adic Hodge theory is the category of continuous representations of the absolute Galois group of…

Many problems of arithmetic nature rely on the computation or analysis of values of $L$-functions attached to objects from geometry. Whilst basic analytic properties of the $L$-functions can be difficult to understand, recent research…

Let \rho be a modulo p representation of the absolute Galois group of a totally real number field. Under the assumptions that \rho has large image and admits a low weight crystalline modular deformation we show that any low weight…

The Iwasawa $\mu$-invariant of the Selmer group of a residually reducible Galois representation arising from a Hecke eigencuspform is studied. Furthermore, certain Iwasawa-invariants refining the $\mu$-invariant are defined and analyzed. As…

Continuing the study of the Iwasawa theory of symmetric powers of CM modular forms at supersingular primes begun by the first author and Antonio Lei, we prove a Main Conjecture equating the "admissible" $p$-adic $L$-functions to…

A central conjecture of Coates and Sujatha predicts that the fine Selmer group of any $p$-adic Galois representation is cotorsion over the relevant Iwasawa algebra with vanishing $\mu$-invariant, generalizing Iwasawa's original conjecture…

Let $E$ be an elliptic curve over $\mathbb Q$ and let $p\geq5$ be a prime of good supersingular reduction for $E$. Let $K$ be an imaginary quadratic field satisfying a modified "Heegner hypothesis" in which $p$ splits, write $K_\infty$ for…

Let $p\geq 5$ be a prime number. In this paper, we construct Galois representations associated with modular forms for which the dimension of the $p$-torsion in the Bloch-Kato Selmer group can be made arbitrarily large. Our result extends…

We consider $\mathbb{Z}_p^{\mathbb{N}}$-extensions $\mathcal{F}$ of a global function field $F$ and study various aspects of Iwasawa theory with emphasis on the two main themes already (and still) developed in the number fields case as…

We study the pro-$p$ Iwahori-Hecke algebra and its Gelfand-Graev modules for the $p$-adic general linear group and its metaplectic covers. We develop the theory of quantum wreath products of skew polynomial type and use it to provide…

We study the behavior of the Iwasawa invariants of the Iwasawa modules which appear in Kato's main conjecture without $p$-adic $L$-functions under congruences. It generalizes the work of Greenberg-Vatsal, Emerton-Pollack-Weston, B.D. Kim,…

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…

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.…

The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual,…

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…

Let $\Lambda$ (isomorphic to $\mathbb{Z}_p[[T]]$) denote the usual Iwasawa algebra and $G$ denote the Galois group of a finite Galois extension $L/K$ of totally real fields. When the non-primitive Iwasawa module over the cyclotomic…

Let E be a finite extension of Fp. Using Fontaine's theory of (phi,Gamma)-modules, Colmez has shown how to attach to any irreducible E-linear representation of Gal(Qpbar/Qp) an infinite dimensional smooth irreducible E-linear representation…