相关论文: On the dihedral main conjectures of Iwasawa theory…

Let f be a cuspidal newform with complex multiplication (CM) and let p be an odd prime at which f is non-ordinary. We construct admissible p-adic L-functions for the symmetric powers of f, thus verifying general conjectures of Dabrowski and…

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…

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…

Ochiai has previously proved that the Beilinson-Kato Euler systems for modular forms interpolate in nearly-ordinary $p$-adic families (Howard has obtained a similar result for Heegner points), based on which he was able to prove a half of…

In this paper, we construct a higher rank Euler system for the multiplicative group over a totally real field by using the Iwasawa main conjecture proved by Wiles. A key ingredient of the construction is to generalize the notion of the…

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…

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…

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 construct a new class of Iwasawa modules, which are the number field analogues of the p-adic realizations of the Picard 1-motives constructed by Deligne in the 1970s and studied extensively from a Galois module structure point of view in…

We build a modified universal Kolyvagin system for the Galois representation attached to a Hida family of modular forms, starting from the big Heegner point Euler system of Longo--Vigni built in towers of Shimura curves. We generalize the…

Let $f$ be a normalized cuspidal eigen-newform of level coprime to $p$ with $a_p(f)=0$. We formulate both integral signed Iwasawa main conjectures and analytic Iwasawa man conjectures attached to the symmetric square motive of $f$ twisted…

We use the theory of reduced determinant functors from [24] to give a new, computationally useful, description of the relative $K_0$-groups of orders in finite dimensional separable algebras that need not be commutative. By combining this…

Given a weight two modular form f with associated p-adic Galois representation V_f, for certain quadratic imaginary fields K one can construct canonical classes in the Galois cohomology of V_f by taking the Kummer images of Heegner points…

In the context of cyclotomic fields, it is still unknown whether there exist Euler systems other than the ones derived from cyclotomic units. Nevertheless, we first give an exposition on how norm-compatible units are generated by any Euler…

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…

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…

We investigate properties of the Euler system associated to certain automorphic representations of the unitary similitude group GU(2,1) with respect to an imaginary quadratic field $E$, constructed by Loeffler-Skinner-Zerbes. By adapting…

This is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic Zp-tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion…

Iwasawa theory of Heegner points on abelian varieties of GL_2 type has been studied by, among others, Mazur, Perrin-Riou, Bertolini and Howard. The purpose of this paper is to describe extensions of some of their results in which abelian…

Let f be a CM modular form and p an odd prime which is inert in the CM field. We construct two p-adic L-functions for the symmetric square of f, one of which has the same interpolating properties as the one constructed by…