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Progress in Mathematics

Motivic Integration

Authors: Chambert-Loir, Antoine, Nicaise, Johannes, Sebag, Julien

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  • Includes the first complete treatment of geometric motivic integration in a monograph Covers the construction of arc schemes and Greenberg schemes
  • Provides a complete discussion of questions concerning the Grothendieck ring of varieties and its algebraic structure
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eBook $109.00
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  • ISBN 978-1-4939-7887-8
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Hardcover $139.99
price for USA in USD
  • ISBN 978-1-4939-7885-4
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  • Usually dispatched within 3 to 5 business days.
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  • ISBN 978-1-4939-9315-4
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About this book

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. 
With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since. 

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-4939-7887-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-1-4939-7885-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover n/a
  • ISBN 978-1-4939-9315-4
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Motivic Integration
Authors
Series Title
Progress in Mathematics
Series Volume
325
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LLC, part of Springer Nature
eBook ISBN
978-1-4939-7887-8
DOI
10.1007/978-1-4939-7887-8
Hardcover ISBN
978-1-4939-7885-4
Softcover ISBN
978-1-4939-9315-4
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XX, 526
Number of Illustrations
47 b/w illustrations
Topics