Related papers: On the Bloch-Kato conjecture for GSp(4)

Let $\rho$ be a conjugate-symplectic, geometric representation of the Galois group of a CM field. Under the assumption that $\rho$ is automorphic, even-dimensional, and of minimal regular Hodge--Tate type, we construct an Euler system for…

We prove Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree $c+2$, with $c=-{1/4}(7\chi+11\sigma)$, for four-manifolds obeying some mild conditions, where $\chi$ and $\sigma$ are their Euler…

Let F be a genus two Siegel newform and g a classical newform, both of squarefree levels and of equal weight l. We prove a pullback formula for certain Eisenstein series -- thus generalizing a construction of Shimura -- and use this to…

We introduce the formalism of Coleman's power series for rank 1 Drinfeld modules and apply it to formulate and prove the analogue of Wiles' explicit reciprocity law in this setting.

We develop an explicit $p$-adic integration theory for Igusa towers of modular Siegel manifolds, which finds applications to explicit reciprocity laws.

Let $f$ be a newform of weight $k\geq 2$, level $N$ with coefficients in a number field $K$, and $A$ the adjoint motive of the motive $M$ associated to $f$. We carefully discuss the construction of the realisations of $M$ and $A$, as well…

In this paper we develop a new method to study Iwasawa theory and Eisenstein families for unitary groups $\mathrm{U}(r,s)$ of general signature over a totally real field $F$. As a consequence we prove that for a motive corresponding to a…

The aim of the present paper is to give evidence, largely numerical, in support of the non-commutative main conjecture of Iwasawa theory for the motive of a primitive modular form of weight k>2 over the Galois extension of Q obtained by…

In this paper, we prove explicit reciprocity laws for a class of formal Drinfeld modules having stable reduction of height one, in the spirit of those existing in characteristic zero (cf. the work of Wiles). We begin by defining the Kummer…

We revisit the construction of Castella and Do of an anticyclotomic Euler system for the $p$-adic Galois representation of a modular form, using diagonal classes. Combining this construction and some previous results of ours, we obtain new…

We show that the cyclotomic Iwasawa--Greenberg Main Conjecture holds for a large class of modular forms with multiplicative reduction at $p$, extending previous results for the good ordinary case. In fact, the multiplicative case is deduced…

We show that the Euler system for the Asai representation corresponding to a Hilbert modular eigenform over a real quadratic field, constructed by Lei, Loeffler and Zerbes (2018), can be interpolated $p$-adically as the Hilbert modular form…

In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that…

We investigate Eisenstein congruences between the so-called Euler systems of Garrett--Rankin--Selberg type. This includes the cohomology classes of Beilinson--Kato, Beilinson--Flach and diagonal cycles. The proofs crucially rely on…

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…

We calculate the constant term of Coleman power series and use it to prove an analogue of Iwasawa Main Conjecture in function fields of characteristic p>0 using Euler systems. This result is proved by a similar method of classical proof of…

We present a novel axiomatic framework for establishing horizontal norm relations in Euler systems that are built from pushforwards of classes in the motivic cohomology of Shimura varieties. This framework is uniformly applicable to the…

Let $K$ be a imaginary quadratic field where the prime $p$ splits. Our goal in this article is to prove results towards the Iwasawa main conjectures for $p$-nearly-ordinary families associated to $\mathrm{GL}_2\times…

We prove a "twist-compatibility" result for p-adic families of cohomology classes associated to symmetric spaces. This shows that a single family of classes (lying in a finitely-generated Iwasawa module) interpolates classical cohomology…

In this paper we use ideas of the non-abelian Iwasawa main conjecture to prove a result about the first Galois cohomology of continuous Galois modules V_p(j) for large Tate-twist j and V_p a Q_p vector space. We show that under a technical…