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Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Rigid Geometry of Curves and Their Jacobians

Authors: Lütkebohmert, Werner

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  • The first comprehensive presentation of the whole topic of curves, Jacobians, abelian varieties and proper analytic group varieties over non-archimedian fields
  • Introduces the powerful tools of formal algebraic geometry as used in arithmetic geometry
  • The book builds a bridge to the more advanced research on the moduli of degeneration of abelian varieties which is a central object in arithmetic geometry
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-27371-6
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-319-27369-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-3-319-80123-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. 

Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.


Reviews

“The work is written in a lucid writing style, and details of proofs are always provided. It contains many important contributions to the literature on rigid geometry, both from the point of view of research and from that of exposition. … The book is therefore highly useful both as a standard reference and as a main resource for an advanced graduate course on rigid geometry.” (Jeroen Sijsling, zbMATH 1387.14003, 2018)

“Werner Lütkebohmert presents in his book the rigid analytic analog of classical topics in complex analysis, namely the theory of compact Riemann surfaces and their Jacobian varieties. … It is a comprehensive exposition of this brilliant theory in a single volume and a must-have for everybody learning or knowing rigid analytic geometry.” (Urs Hartl, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 119, 2017)


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-27371-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-319-27369-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-3-319-80123-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Rigid Geometry of Curves and Their Jacobians
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
61
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-27371-6
DOI
10.1007/978-3-319-27371-6
Hardcover ISBN
978-3-319-27369-3
Softcover ISBN
978-3-319-80123-0
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XVIII, 386
Number of Illustrations
1 b/w illustrations
Topics