Rigid Geometry of Curves and Their Jacobians - Werner Lütkebohmert

Rigid Geometry of Curves and Their Jacobians

Buch | Hardcover
XVIII, 386 Seiten
2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-27369-3 (ISBN)
149,79 inkl. MwSt

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.




"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)

Erscheinungsdatum
Reihe/Serie Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Zusatzinfo XVIII, 386 p. 1 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte Algebraic Geometry • Algebraische Geometrie • Arithmetic Geometry • Commutative rings and algebras • Kurven • mathematics and statistics • mathematics, general • Number Theory • Several Complex Variables and Analytic Spaces
ISBN-10 3-319-27369-8 / 3319273698
ISBN-13 978-3-319-27369-3 / 9783319273693
Zustand Neuware
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