Links Between Cyclotomic and GL 2 Iwasawa Theory
نویسندگان
چکیده
We study, in the case of ordinary primes, some connections between the GL2 and cyclotomic Iwasawa theory of an elliptic curve without complex multiplication. 2000 Mathematics Subject Classification: 11G05; 11R23.
منابع مشابه
Globally 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 کاملArithmetic incarnations of zeta in Iwasawa theory
We give a brief exposition of the Iwasawa theory of cyclotomic extensions, so as to discuss its relationship with p-adic zeta functions. We give an overview of these connections and the arithmetic significance of the theory, leading up to a statement of the main conjecture.
متن کاملCyclotomic Units and the Iwasawa Main Conjecture
In these notes, we follow the proof in [1] of the main conjecture of Iwasawa theory making heavy use of the Euler system of cyclotomic units. On the one hand, using the local theory of Coleman series and ideas of Iwasawa one obtains a connection with the p-adic zeta function. On the other hand by CFT and Rubin’s refinement of the ideas of Kolyvagin (and the analytic class number formula) one ob...
متن کاملSome New Ideals in Classical Iwasawa Theory
We construct an analogue of the Stickelberger ideal for real abelian fields by means of cyclotomic units and a Kummer-type pairing with values in a completed p-adic group-ring. We give several different descriptions of this ideal, prove the analogue of Stickelberger's Theorem using Thaine's methods and establish links with certain Fitting ideals in a particular case. Our construction fits into ...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003