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Rigid Geometry of Curves and Their Jacobians

Rigid Geometry of Curves and Their Jacobians by Werner Lütkebohmert
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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.


Springer International Publishing; January 2016
398 pages; ISBN 9783319273716
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Title: Rigid Geometry of Curves and Their Jacobians
Author: Werner Lütkebohmert
 
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9783319273693
9783319273716