Related papers: On the Iwasawa main conjectures for modular forms …

Let f be a newform of weight 2k-2 and level 1. In this paper we provide evidence for the Bloch-Kato conjecture for modular forms. We demonstrate an implication that under suitable hypothesis if a prime divides the algebraic part of L(k,f),…

Given an odd prime number $p$ and a $p$-stabilized Artin representation $\rho$ over $\mathbb{Q}$, we introduce a family of $p$-adic Stark regulators and we formulate an Iwasawa-Greenberg main conjecture and a $p$-adic Stark conjecture which…

We prove an equivariant version of Beilinson's conjecture on non-critical $L$-values of strongly modular abelian varieties over number fields. As an application, we prove a weak version of Zagier's conjecture on $L(E,2)$ and Deninger's…

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 $L(E/K,s)$,…

Let F be a global function field of characteristic p with ring of integers A and let \Phi be a Hayes module on the Hilbert class field H(A) of F. We prove an Iwasawa Main Conjecture for the Z_p^\infty-extension F/F generated by the…

Let $\Pi$ be a cuspidal automorphic representation of $\mathrm{GL}_{2n}(\mathbb{A_Q})$ and let $p$ be an odd prime at which $\Pi$ is unramified. In a recent work, Barrera, Dimitrov and Williams constructed possibly unbounded $p$-adic…

For a real quadratic field $K=\mathbb{Q}(\sqrt{D})$, let $K_{\infty}$ denote the cyclotomic $\mathbb{Z}_{p}$-extension of $K$. Greenberg conjectured that the corresponding Iwasawa module $X_{\infty}$ is finite. Building on the work of…

We present certain results on the Iwasawa theory of an abelian variety with potentially good ordinary reduction at all primes above $p$. These are then applied to study Diophantine stability and integally Diophantine extensions. Along the…

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…

We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings…

We extend Kobayashi's formulation of Iwasawa theory for elliptic curves at supersingular primes to include the case $a_p \neq 0$, where $a_p$ is the trace of Frobenius. To do this, we algebraically construct $p$-adic $L$-functions…

We prove faithfulness of infinite-dimensional generalised Verma modules for Iwasawa algebras corresponding to split simple Lie algebras with a Chevalley basis. We use this to prove faithfulness of all infinite-dimensional highest-weight…

We discuss abelian equivariant Iwasawa theory for elliptic curves over $\mathbb{Q}$ at good supersingular primes and non-anomalous good ordinary primes. Using Kobayashi's method, we construct equivariant Coleman maps, which send the…

The theta-block conjecture proposed by Gritsenko--Poor--Yuen in 2013 characterizes Siegel paramodular forms which are simultaneously Borcherds products and additive Jacobi lifts. In this paper, we prove this conjecture for two new infinite…

Let $p$ be a prime and $\mathcal{K}$ be an imaginary quadratic field. In this paper we generalize a recent construction of a new type of $p$-adic $L$-function and $p$-adic Waldspurger formula by Andreatta-Iovita for $p$ non-split in…

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…

Recently, D. Burns and C. Greither (Invent. Math., 2003) deduced an equivariant version of the main conjecture for abelian number fields. This was the key to their proof of the equivariant Tamagawa number conjecture. A. Huber and G. Kings…

Recently Ritter and Weiss introduced an equivariant "main conjecture" than generalizes and refines the Main Conjecture of Iwasawa theory. In this paper, we show that, for the prime 2 and a dihedral extension of order 8 over Q, this…

In this paper we construct an infinite family of paramodular forms of weight $2$ which are simultaneously Borcherds products and additive Jacobi lifts. This proves an important part of the theta-block conjecture of Gritsenko--Poor--Yuen…

In this article, we study the p-ordinary Iwasawa theory of the (conjectural) Rubin-Stark elements defined over abelian extensions of a CM field F and develop a rank-g Euler/Kolyvagin system machinery (where 2g is the degree of F), refining…