Related papers: Wach modules and Iwasawa theory for modular forms

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…

The $p^\infty$-fine Selmer group of an elliptic curve $E$ over a number field $F$ is a subgroup of the classical $p^\infty$-Selmer group of $E$ over $F$. Fine Selmer group is closely related to the 1st and 2nd Iwasawa cohomology groups.…

Let l be an odd prime and K/k a Galois extension of totally real number fields with Galois group G such that K/k_\infty and k/Q are finite. We give a full description of the algebraic structure of the semisimple algebra QG=Quot(\Lambda G)…

Let F be a number field with adele ring A_F, and \pi an isobaric, algebraic automorphic representation of GL_4(A_F) of a fixed archimedean weight, which is quasi-regular, meaning that at every archimedean place v of F, the 4-dimensional…

For the $p$-cyclotomic tower of $\mathbb{Q}_p$ Fontaine established a description of local Iwasawa cohomology with coefficients in a local Galois representation $V$ in terms of the $\psi$-operator acting on the attached etale…

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 study Galois descent of K_1 of group algebras with coefficients in certain subrings of the ring of integers of C_p, the completion of an algebraic closure of Q_p.

Let $F$ be a number field unramified at an odd prime $p$ and $F_\infty$ be the $\mathbf{Z}_p$-cyclotomic extension of $F$. Generalizing Kobayashi plus/minus Selmer groups for elliptic curves, B\"uy\"ukboduk and Lei have defined modified…

We construct $p$-adic $L$-functions associated with $p$-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in $p$-adic families, and does…

Motives and automorphic forms of arithmetic type give rise to Galois representations that occur in {\it compatible families}. These compatible families are of p-adic representations with p varying. By reducing such a family mod p one…

Let $E_{/\mathbb{Q}}$ be an elliptic curve and $p$ be an odd prime number at which $E$ has good ordinary reduction. Let $Sel_{p^\infty}(\mathbb{Q}_\infty, E)$ denote the $p$-primary Selmer group of $E$ considered over the cyclotomic…

We consider questions in Galois cohomology which arise by considering mod $p$ Galois representations arising from automorphic forms. We consider a Galois cohomological analog for the standard heuristics about the distribution of Wieferich…

Let $E/\mathbb{Q}$ be an elliptic curve and $p$ an odd prime where $E$ has good supersingular reduction. Let $F_1$ denote the characteristic power series of the Pontryagin dual of the fine Selmer group of $E$ over the cyclotomic…

In this paper, we prove the Iwasawa main conjecture of totally real fields for certain specific non-commutative $p$-adic Lie extensions, using the integral logarithms introduced by Oliver and Taylor. Our result gives certain generalization…

We construct a new Euler system for the Galois representation $V_{f,\chi}$ attached to a newform $f$ of weight $2r\geq 2$ twisted by an anticyclotomic Hecke character $\chi$. The Euler system is anticyclotomic in the sense of…

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 $E/\mathbb{Q}$ be an elliptic curve with ordinary reduction at a prime $p$, and let $K$ be an imaginary quadratic field. The anticyclotomic Iwasawa main conjecture, depending upon the sign of the functional equation of $L(E/K,s)$,…

The point of this paper is to give an explicit p-adic analytic construction of two Iwasawa functions L_p^\sharp(f,T) and L_p^\flat(f,T) for a weight two modular form \sum a_n q^n and a good prime p. This generalizes work of Pollack who…

The primary objective of this paper is the study of different instances of the elliptic Stark conjectures of Darmon, Lauder and Rotger, in a situation where the elliptic curve attached to the modular form $f$ has split multiplicative…

We develop the topological polylogarithm which provides an integral version of Nori's Eisenstein cohomology classes for $GL_n(\mathbf{Z})$ and yields classes with values in an Iwasawa algebra. This implies directly the integrality…