Authors:
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 61)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
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
“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)
Authors and Affiliations
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Institute of Pure Mathematics, Ulm University, Ulm, Germany
Werner Lütkebohmert
Bibliographic Information
Book Title: Rigid Geometry of Curves and Their Jacobians
Authors: Werner Lütkebohmert
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
DOI: https://doi.org/10.1007/978-3-319-27371-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-27369-3Published: 03 February 2016
Softcover ISBN: 978-3-319-80123-0Published: 30 March 2018
eBook ISBN: 978-3-319-27371-6Published: 26 January 2016
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 1
Number of Pages: XVIII, 386
Number of Illustrations: 1 b/w illustrations
Topics: Algebraic Geometry, Several Complex Variables and Analytic Spaces