Introduction to Iwasawa Theory
نویسنده
چکیده
منابع مشابه
Iwasawa theory and generalizations
This is an introduction to Iwasawa theory and its generalizations. We discuss some main conjectures and related subjects. Mathematics Subject Classification (2000). Primary 11R23; Secondary 11G40, 14G10.
متن کاملIWASAWA THEORY OF TOTALLY REAL FIELDS FOR CERTAIN NON-COMMUTATIVE p-EXTENSIONS
In this paper, we prove the Iwasawa main conjecture (in the sense of [CFKSV]) of totally real fields for certain specific noncommutative p-adic Lie extensions, using the integral logarithms introduced by Oliver and Taylor. Our result gives certain generalization of Kato’s proof of the main conjecture for Galois extensions of Heisenberg type ([Kato1]). 0. Introduction 0.
متن کاملDuality Theorems in the Multivariable Iwasawa Theory of Number Fields
1. Introduction. Let K be a number field, let p be an odd prime, and let K ∞ /K be an extension containing all p-power roots of unity whose Galois group Γ is isomorphic to Z
متن کاملGlobally analytic $p$-adic representations of the pro--$p$--Iwahori subgroup of $GL(2)$ and base change, I : Iwasawa algebras and a base change map
This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2, mathbb{Z}_p)$. It then describes a natural base change map between the Iwasawa algebras or more correctly, as it turns out, between the global distribut...
متن کاملSelmer Groups and the Eisenstein-klingen Ideal
0 Introduction The central point in the Bloch-Kato conjectures is to establish formulas for the order of the Selmer groups attached to Galois representations in terms of the special values of their L-functions. In order to give upper bound, the main way is to construct Euler systems following Kolyvagin. Besides, lower bounds have been obtained by using congruences between automorphic forms. So,...
متن کامل