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Algebraic Patching

  • Moshe¬†Jarden

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XXIII
  2. Moshe Jarden
    Pages 1-9
  3. Moshe Jarden
    Pages 10-30
  4. Moshe Jarden
    Pages 31-42
  5. Moshe Jarden
    Pages 61-97
  6. Moshe Jarden
    Pages 98-128
  7. Moshe Jarden
    Pages 142-163
  8. Moshe Jarden
    Pages 164-206
  9. Moshe Jarden
    Pages 207-232
  10. Moshe Jarden
    Pages 252-274
  11. Back Matter
    Pages 275-290

About this book

Introduction

Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields". Among others, it leads to the solution of two central results in "Field Arithmetic": (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$.

Keywords

Absolute Galois Group Ample Field Field Arithmetic Finite Split Embedding Problem Free Profinite Group

Authors and affiliations

  • Moshe¬†Jarden
    • 1
  1. 1., School of MathematicsTel Aviv UniversityRamat AvivIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-15128-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-15127-9
  • Online ISBN 978-3-642-15128-6
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site