Titlebook: Iwasawa Theory 2012; State of the Art and Thanasis Bouganis,Otmar Venjakob Conference proceedings 2014 Springer-Verlag Berlin Heidelberg 20

Femish

Overview of Some Iwasawa Theoryon of the class group in .-extensions and the case of elliptic curves. For both, we give a description of the basic results and reach a formulation of the main conjecture. Furthermore a sketch of the leading term formula for the characteristic series for an elliptic curve, a hint at generalisations

IOTA

发微光

On Extra Zeros of ,-Adic ,-Functions: The Crystalline Caseath 133:1573–1632, 2011) to include non-critical values. We prove that this conjecture is compatible with Perrin-Riou’s theory of .-adic .-functions. Namely, using Nekovář’s machinery of Selmer complexes we prove that our .-invariant appears as an additional factor in the Bloch–Kato type formula for

不能约

On Special ,-Values Attached to Siegel Modular Forms Siegel modular forms. These results are all stated over an algebraic closure of .. In this article we work out the field of definition of these special values. In this way we extend some previous results obtained by Sturm, Harris, Panchishkin, and Böcherer-Schmidt.

Notorious

Modular Symbols in Iwasawa Theory., there is an explicit conjecture of the third author relating the geometry of modular curves and the arithmetic of cyclotomic fields, and it is proven in many instances by the work of the first two authors. The paper is divided into three parts: in the first, we explain the conjecture of the third

反省

On ,-Adic Artin ,-Functions II Mazur and Wiles in Mazur and Wiles (1984). Wiles later proved a far-reaching generalization involving .-adic .-functions for Hecke characters of finite order for a totally real number field in Wiles (1990). As we discussed in Greenberg (1983), an analogue of Iwasawa’s conjecture for .-adic Artin .-

抒情短诗

The ,-Adic Height Pairing on Abelian Varieties at Non-ordinary Primes norm subgroup. In this paper, we generalize his construction to the non-ordinary case and compare it with that of Zarhin-Nekovár̆. As an application, we generalize the .-adic Gross-Zagier formula in Kobayashi (Invent Math 191(3):527–629, 2013) to newforms for ..(.) of weight 2 with . Fourier coeffi

Deadpan

Iwasawa Modules Arising from Deformation Spaces of ,-Divisible Formal Group Laws universal deformation space of . give rise to pseudocompact modules over the Iwasawa algebra of the automorphism group of .. Passing to global rigid analytic sections, we obtain representations which are topologically dual to locally analytic representations. In studying these, one is led to the co

BARGE

The Structure of Selmer Groups of Elliptic Curves and Modular Symbolsnts. In our previous paper Kurihara (Refined Iwasawa theory for .-adic representations and the structure of Selmer groups. Münster J Math ., to appear), assuming the main conjecture and the non-degeneracy of the .-adic height pairing, we proved that the structure of the Selmer group with respect to

SLUMP