Contributions in Mathematical and Computational Sciences

The Arithmetic of Fundamental Groups

PIA 2010

Editors: Stix, Jakob (Ed.)

  • The book contains the lecture notes of the Heidelberg lectures on fundamental groups/on Coleman integration. These are introductory texts aiming to familiarize non-specialists with essential techniques of the subject
  • An important development in Minhyong Kim's non-abelian Chabauty method by introducing the motivic fundamental group into the subject is reported on by Gerd Faltings and Majid Hadian
  • The book contains current research on important questions in the arithmetic of fundamental groups
see more benefits

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-3-642-23905-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-3-642-23904-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-3-642-43942-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

In the more than 100 years since the fundamental group was first introduced by Henri Poincaré it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and its analogies have found numerous applications in mathematics that are still being investigated today, and which are explored in this volume, the result of a meeting at Heidelberg University that brought together mathematicians who use or study fundamental groups in their work with an eye towards applications in arithmetic. The book acknowledges the varied incarnations of the fundamental group: pro-finite, ℓ-adic, p-adic, pro-algebraic and motivic. It explores a wealth of topics that range from anabelian geometry (in particular the section conjecture), the ℓ-adic polylogarithm, gonality questions of modular curves, vector bundles in connection with monodromy, and relative pro-algebraic completions, to a motivic version of Minhyong Kim's non-abelian Chabauty method and p-adic integration after Coleman. The editor has also included the abstracts of all the talks given at the Heidelberg meeting, as well as the notes on Coleman integration and on Grothendieck's fundamental group with a view towards anabelian geometry taken from a series of introductory lectures given by Amnon Besser and Tamás Szamuely, respectively.

Table of contents (14 chapters)

  • Heidelberg Lectures on Coleman Integration

    Besser, Amnon

    Pages 3-52

  • Heidelberg Lectures on Fundamental Groups

    Szamuely, Tamás

    Pages 53-74

  • Vector Bundles Trivialized by Proper Morphisms and the Fundamental Group Scheme, II

    Biswas, Indranil (et al.)

    Pages 77-88

  • Note on the Gonality of Abstract Modular Curves

    Cadoret, Anna

    Pages 89-106

  • The Motivic Logarithm for Curves

    Faltings, Gerd

    Pages 107-125

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-3-642-23905-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-3-642-23904-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-3-642-43942-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
The Arithmetic of Fundamental Groups
Book Subtitle
PIA 2010
Editors
  • Jakob Stix
Series Title
Contributions in Mathematical and Computational Sciences
Series Volume
2
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-23905-2
DOI
10.1007/978-3-642-23905-2
Hardcover ISBN
978-3-642-23904-5
Softcover ISBN
978-3-642-43942-1
Series ISSN
2191-303X
Edition Number
1
Number of Pages
XII, 380
Topics