Rigid Geometry of Curves and Their Jacobians

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Beschreibung

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.

Zusammenfassung

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: [...]

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2016
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Inhalt:	xviii 386 S. 1 s/w Illustr. 386 p. 1 illus.
ISBN-13:	9783319273693
ISBN-10:	3319273698
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Lütkebohmert, Werner
Auflage:	1st ed. 2016
Hersteller:	Springer International Publishing Springer International Publishing AG Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Maße:	241 x 160 x 28 mm
Von/Mit:	Werner Lütkebohmert
Erscheinungsdatum:	03.02.2016
Gewicht:	0,77 kg

Artikel-ID: 104114588