Refined Iwasawa theory and Kolyvagin systems of Gauss sum type

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Refined Iwasawa theory and Kolyvagin systems of Gauss sum type

In this paper, we establish a refinement of the usual Iwasawa main conjecture for the ideal class groups of CM-fields over a totally real field, using higher Fitting ideals.

متن کامل

Refined Class Number Formulas and Kolyvagin Systems

We use the theory of Kolyvagin systems to prove (most of) a refined class number formula conjectured by Darmon. We show that for every odd prime p, each side of Darmon’s conjectured formula (indexed by positive integers n) is “almost” a p-adic Kolyvagin system as n varies. Using the fact that the space of Kolyvagin systems is free of rank one over Zp, we show that Darmon’s formula for arbitrary...

متن کامل

Heegner Point Kolyvagin System and Iwasawa Main Conjecture

In this paper we prove an anticyclotomic Iwasawa main conjecture proposed by PerrinRiou for Heegner points when the global sign is −1, using a recent work of the author on one divisibility of Iwasawa-Greenberg main conjecture for Rankin-Selberg p-adic L-functions. As a byproduct we also prove the equality for the above mentioned main conjecture under some local conditions, and an improvement of...

متن کامل

Refined Iwasawa theory for p-adic representations and the structure of Selmer groups

In this paper, we develop the idea in [16] to obtain finer results on the structure of Selmer modules for p-adic representations than the usual main conjecture in Iwasawa theory. We determine the higher Fitting ideals of the Selmer modules under several assumptions. Especially, we describe the structure of the classical Selmer group of an elliptic curve over Q, using the ideals defined from mod...

متن کامل

Introduction to Kolyvagin systems

Since their introduction by Kolyvagin in [Ko], Euler systems have been used in several important applications in arithmetic algebraic geometry. For a p-adic Galois module T , Kolyvagin’s machinery is designed to provide an upper bound for the size of a Selmer group associated to the Cartier dual of T . Kolyvagin’s method proceeds in three steps. The first step is to establish an Euler system as...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Proceedings of the London Mathematical Society

سال: 2011

ISSN: 0024-6115

DOI: 10.1112/plms/pdr044