Iwasawa Theory 2012

State of the Art and Recent Advances

  • Thanasis Bouganis
  • Otmar Venjakob
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 7)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Lecture Notes

  3. Research and Survey Articles

    1. Front Matter
      Pages 63-63
    2. Takako Fukaya, Kazuya Kato, Romyar Sharifi
      Pages 177-219
    3. Takashi Fukuda, Keiichi Komatsu, Takayuki Morisawa
      Pages 221-226
    4. Ralph Greenberg
      Pages 227-245
    5. Thong Nguyen Quang Do
      Pages 379-399
    6. Eric Urban
      Pages 401-441
    7. Zdzisław Wojtkowiak
      Pages 471-483
  4. Takako Fukaya, Kazuya Kato, Romyar Sharifi
    Pages E1-E1

About these proceedings

Introduction

This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory.

Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida’s theory of p-adic modular forms and big Galois representations play a crucial part. 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).

Keywords

Iwasawa theory Selmer groups automorphic forms complex and p-adic L-functions

Editors and affiliations

  • Thanasis Bouganis
    • 1
  • Otmar Venjakob
    • 2
  1. 1.Dept. of Mathematical SciencesDurham UniversityDurhamUnited Kingdom
  2. 2.Institute of MathematicsUniversity of HeidelbergHeidelbergGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-55245-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-55244-1
  • Online ISBN 978-3-642-55245-8
  • Series Print ISSN 2191-303X
  • Series Online ISSN 2191-3048
  • About this book