Related papers: $p$-adic $L$-functions for elliptic curves over gl…

If E is an elliptic curve defined over a number field and p is a prime of good ordinary reduction for E, a theorem of Rubin relates the p-adic height pairing on the p-power Selmer group of E to the first derivative of a cohomologically…

Consider an abelian variety $A$ defined over a global field $K$ and let $L/K$ be a $\Z_p^d$-extension, unramified outside a finite set of places of $K$, with $\Gal(L/K)=\Gamma$. Let $\Lambda(\Gamma):=\Z_p[[\Gamma]]$ denote the Iwasawa…

Let $E/\mathbb{Q}$ an elliptic curve with good supersingular reduction at a prime $p\geq 5$, and $K$ an imaginary quadratic field such that the root number of $E$ over $K$ equals $-1$. When $p$ splits in $K$, Castella and Wan formulated the…

Let $A$ be an abelian variety defined over a global field $F$ of positive characteristic $p$ and let $\calf/F$ be a $\Z_p^{\N}$-extension, unramified outside a finite set of places of $F$. Assuming that all ramified places are totally…

Given an elliptic curve E and a prime p of (good) supersingular reduction, we formulate p-adic analogues of the Birch and Swinnerton-Dyer conjecture using a pair of Iwasawa functions L^\sharp(E,T) and L^\flat(E,T). They are equivalent to…

In the present paper, we study the $p$-adic $L$-functions and the (strict) Selmer groups over $\mathbb{Q}_{\infty}$, the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$, of the $p$-adic weight one cusp forms $f$, obtained via the…

We prove an analogue of Kida's formula for the Iwasawa invariants of the Mazur-Tate elements attached to elliptic curves over $\mathbb{Q}$. Let $p$ be an odd prime and let $L/K$ be a Galois extension of abelian number fields with $p$-power…

In this paper, we generalize two results of H. Darmon and V. Rotger on triple product $p$-adic $L$-functions associated with Hida families to finite slope families. We first prove a $p$-adic Gross-Zagier formula, then demonstrate an…

Let $K$ be an imaginary quadratic field and $p$ be an odd prime number. Let $E/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$. We study the Iwasawa theory of $E$ over the anticyclotomic $\mathbb{Z}_p$-extension of $K$…

The goal of this article is to obtain a proof of the Main conjectures of Iwasawa theory for rational elliptic curves over anticyclotomic extensions of imaginary quadratic fields, under mild arithmetic assumptions, both in the case where the…

We construct a $p$-adic $L$-function for $P$-ordinary Hida families of cuspidal automorphic representations on a unitary group $G$. The main new idea of our work is to incorporate the theory of Schneider-Zink types for the Levi quotient of…

For an algebraic Hecke character defined on a CM field $F$ of degree $2d$, Katz constructed a $p$-adic $L$-function of $d+1+\delta_{F,p}$ variables in his innovative paper published in 1978, where $\delta_{F,p}$ denotes the Leopoldt defect…

Let $E/\mathbb{Q}$ be an elliptic curve and let $p$ be an odd prime of good reduction for $E$. Let $K$ be an imaginary quadratic field satisfying the classical Heegner hypothesis and in which $p$ splits. The goal of this paper is two-fold:…

Let $E/K$ be a finite Galois extension of totally real number fields with Galois group $G$. Let $p$ be an odd prime and let $r>1$ be an odd integer. The $p$-adic Beilinson conjecture relates the values at $s=r$ of $p$-adic Artin…

In this note we propose a new construction of cyclotomic p-adic L-functions attached to classical modular cuspidal eigenforms. This allows us to cover most known cases to date and provides a method which is amenable to generalizations to…

We formulate integral Iwasawa main conjectures for suitable twists of a newform $f$ that is non-ordinary at $p$, over the cyclotomic $\mathbb{Z}_p$-extension, the anticyclotomic $\mathbb{Z}_p$-extensions (in both the definite and the…

Let $p$ be an odd prime, $ f$ be a $ p $-ordinary newform of weight $ k $ and $ h $ be a normalized cuspidal $ p $-ordinary Hecke eigenform of weight $ l < k$. In this article, we study the $p$-adic $ L $-function and $ p^{\infty} $-Selmer…

We formulate a new equivariant Main Conjecture in Iwasawa theory of number fields and study its properties. This is done for arbitrary one-dimensional $p$-adic Lie extensions $L_\infty/K$ containing the cyclotomic $\mathbb{Z}_p$-extension…

In this article, we discuss Iwasawa Main Conjecture for $p$-adic families of elliptic modular cuspforms. After the overview on the situation of the ordinary case of Hida family, we will introduce a Coleman map for Coleman family for the…

Let $A$ be an abelian variety over a global field $K$ of characteristic $p \ge 0$. If $A$ has nontrivial (resp. full) $K$-rational $l$-torsion for a prime $l \neq p$, we exploit the fppf cohomological interpretation of the $l$-Selmer group…