An Introduction to Iwasawa Theory

Fichier PDF

Iwasawa Modules The Main Conjecture An Introduction to Iwasawa Theory Jordan Schettler University of California, Santa Barbara?/?/2012, Cyclotomic Fields Zp-Extensions Iwasawa Modules The Main Conjecture Outline 1 Cyclotomic Fields 2 Zp-Extensions 3 Iwasawa Modules 4 The Main Conjecture, Cyclotomic Fields Zp-Extensions Iwasawa Modules The Main Conjecture Cyclotomic Fields, …

Introduction to Iwasawa Theory

Fichier PDF

Introduction to Iwasawa Theory Yi Ouyang Department of Mathematical Sciences Tsinghua University Beijing, China 100084 Email: youyang@math,tsinghua,edu,cn, Contents 1 Modules up to pseudo-isomorphism 2 2 Iwasawa modules 8 3 Z p-extensions 15 4 Iwasawa theory of elliptic curves 23 1, Chapter 1 Modules up to pseudo-isomorphism Let Abe a commutative noetherian integrally closed …

An Introduction to Iwasawa Theory

Fichier PDF

An Introduction to Iwasawa Theory , Iwasawa theory grew out of Kenkichi Iwasawa’s efforts 1950s – 1970s to transfer to in this course is to explain the general philosophy of Iwasawa theory, state the “main conjecture” in the particular case of Dirichlet functions, give a rough outline of its proof and , L-conclude with some concrete arithmetic applications, open problems and new

Nesin Köyleri

Title of the course: Introduction to Iwasawa theory Instructor: Dr, José-Ibrahim Villanueva-Gutiérrez Institution: Universität Heidelberg Dates: 23-29 September 2019 Prerequisites: Algebra II, Topology, Analysis Level: Advanced undergraduate Abstract: The fundamental theorem of arithmetic states that each integer can be written in a unique way as a product of units and powers of prime numbers,

Part I

Fichier PDF

AN INTRODUCTION TO IWASAWA THEORY FOR ELLIPTIC CURVES Abstract, We present the rst few sections of Greenberg’s article \Introduction to Iwasawa Theory for Elliptic Curves”, In the process, we review the construction of Z p-extensions of the rational numbers, discuss Iwasawa’s result on the growth of the class group in towers of cyclotomic extensions, and analyze the notion of a Selmer

Romyar Sharifi

Fichier PDF

Let us end this introduction by mentioning the two of the major directions in which Iwasawa theory has expanded over the years, As a first and obvious course of action, one can replace our limits of class groups with more general objects, Via class field theory, we note that the Pontryagin dual X_ ¥ may be identified with the kernel of the

TOPICS IN IWASAWA THEORY

Fichier PDF

TOPICS IN IWASAWA THEORY Ralph Greenberg December 15, 2006 1 Ideal class groups, The ideal class group of a number field F is defined as the quotient group ClF = FF/PF, where FF denotes the group of fractional ideals of Fand PF denotes the subgroup of principal fractional ideals, It has been an object of intense study since the nineteenth century, One of the fundamental theorems of algebraic

The Iwasawa Main Conjecture: an approach via Euler Systems

Fichier PDF

an introduction to Infinite Galois theory and the corresponding Ramification theory, Next, we show how to prove the Iwasawa’s theorem about ideal class groups in Z ￿-extensions, using the approaches of [Wa] and [Bro], Furthermore, we define the orthogonal idempotents and we study some consequences of the decomposition that they produce on Λ-modules, following [Sa3], Finally, as an

TCC Iwasawa theory

Structure theory of Zp[[T]]-modules, Iwasawa‘s control theory on Zp-extensions, p-adic measures and the p-adic zeta function, Coleman power series, The Iwasawa theorem, TBD: either “A short introduction to Euler systems” or “A short introduction to Hida theory“, discussing the relations with the Iwasawa main conjecture,

Théorie d’Iwasawa — Wikipédia

Généralités

INTRODUCTION TO IWASAWA THEORY

INTRODUCTION TO IWASAWA THEORY, January 2006; Authors: Keiichi Komatsu, Keiichi Komatsu, This person is not on ResearchGate, or hasn’t claimed …

Iwasawa Theory 2012

Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed, This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012, In particular it offers an introduction to Iwasawa theory based on a preparatory course by Chris Wuthrich and a survey of the proof of Skinner & Urban based on a lecture course by Xin Wan,

Iwasawa theory

Iwasawa theory, A theory of $\mathbf {Z} _ { p }$-extensions introduced by K, Iwasawa [a8], Its motivation has been a strong analogy between number fields and curves over finite fields, One of the most fruitful results in this theory is the Iwasawa main conjecture, which has been proved for totally real number fields [a19],

Introduction to Cyclotomic Fields

Introduction to Cyclotomic Fields is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory, Starting at an elementary level, the volume covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa‘s theory of Z_p-extensions, leading the reader to an understanding of modern research