Related papers: Congruences between Hilbert modular forms of weigh…

We prove one divisibility relation of the anticyclotomic Iwasawa Main Conjecture for a higher weight ordinary modular form $f$ and an imaginary quadratic field satisfying a "relaxed" Heegner hypothesis. Let $\Lambda$ be the anticyclotomic…

We consider mod $p$ Hilbert modular forms for a totally real field $F$, viewed as sections of automorphic line bundles on Hilbert modular varieties in prime characteristic $p$. For a Hecke eigenform of arbitrary weight, we prove the…

Our main result in this article is a proof (under mild technical assumptions) of an analogue for $p$-adic Galois representations attached to a newform $f$ of even weight $k\geq4$ of Kolyvagin's conjecture on the $p$-indivisibility of…

Let $\ell$ be a rational prime and let $p:Y\rightarrow X$ be a Galois cover of finite graphs whose Galois group is a finite $\ell$-group. Consider a $\mathbb{Z}_{\ell}$-tower above $X$ and its pullback along $p$. Assuming that all the…

We establish formulae for the Iwasawa invariants of Mazur--Tate elements of cuspidal eigenforms, generalizing known results in weight 2. Our first theorem deals with forms of "medium" weight, and our second deals with forms of small slope .…

The Morita equivalence of m-regular involutive quantales in the context of the theory of Hilbert $A$-modules is presented. The corresponding fundamental representation theorems are shown. We also prove that two commutative m-regular…

We generalise a result by Greenberg and Vatsal on the relation between the analytic $\mu$-invariants of two elliptic curves whose $p^i$-torsion subgroups are isomorphic as Galois modules, for suitable $i$.

In this article, we construct zeta morphisms for the universal deformations of odd absolutely irreducible two dimensional mod p Galois representations satisfying some mild assumptions, and prove that our zeta morphisms interpolate Kato's…

We construct p-adic L-functions associated to cuspidal Hilbert modular eigenforms of parallel weight two in certain dihedral or anticyclotomic extensions via the Jacquet-Langlands correspondence, generalizing works of Bertolini-Darmon,…

We extend the main result of [Math. Res. Lett. 15 (2008), 715-725] to Galois extensions L/K of totally real number fields of arbitrary odd prime power degree, thereby offering support for the validity of the 'main conjecture' of equivariant…

We construct a bipartite Euler system in the sense of Howard for Hilbert modular eigenforms of parallel weight two over totally real fields, generalizing works of Bertolini-Darmon, Longo, Nekovar, Pollack-Weston and others. The construction…

In this note, we compare the dual Selmer groups of an abelian variety with that of its dual over certain large Galois field. We give formula which relates the generalized Iwasawa $\mu$-invariants associated with their dual Selmer groups…

Let $E_{/\mathbb{Q}}$ be an elliptic curve and $p$ an odd prime such that $E$ has good ordinary reduction at $p$ and the Galois representation on $E[p]$ is irreducible. Then Greenberg's $\mu=0$ conjecture predicts that the Selmer group of…

We study the Iwasawa main conjecture for quadratic Hilbert modular forms over the p-cyclotomic tower. Using an Euler system in the cohomology of Siegel modular varieties, we prove the "Kato divisibility" of the Iwasawa main conjecture under…

The aim of this paper is to prove inequalities towards instances of the Bloch-Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the $L$-function at the central point is zero or one. We achieve…

The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight 1 and level prime to p is unramified above p. This includes the important case of…

We prove a slight generalization of Iwasawa's `Riemann-Hurwitz' formula for number fields and use it to generalize Ferrero's and Kida's well-known computations of Iwasawa \lambda-invariants for the cyclotomic Z_2-extensions of imaginary…

Let F be a totally real field and p an odd prime. If r is a continuous, semisimple, totally odd mod p representation of the absolute Galois group of F which is tamely ramified at all places of F dividing p, then we formulate a conjecture…

Let $K_\infty/K$ be a uniform $p$-adic Lie extension. We compare several arithmetic invariants of Iwasawa modules of ideal class groups on the one side and fine Selmer groups of abelian varieties on the other side. If $K_\infty$ contains…

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…