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Rigid geometry of curves and their J...

Lutkebohmert, Werner.

Rigid geometry of curves and their Jacobians

Record Type:	Electronic resources : Monograph/item
Title/Author:	Rigid geometry of curves and their Jacobiansby Werner Lutkebohmert.
Author:	Lutkebohmert, Werner.
Published:	Cham :Springer International Publishing :2016.
Description:	xviii, 386 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Curves, Plane.
Online resource:	http://dx.doi.org/10.1007/978-3-319-27371-6
ISBN:	9783319273716$q(electronic bk.)

Rigid geometry of curves and their Jacobians
Lutkebohmert, Werner.

Rigid geometry of curves and their Jacobians[electronic resource] /by Werner Lutkebohmert. - Cham :Springer International Publishing :2016. - xviii, 386 p. :ill., digital ;24 cm. - Ergebnisse der Mathematik und ihrer Grenzgebiete,3. folge, v.610071-1136 ;. - Ergebnisse der Mathematik und ihrer Grenzgebiete ;3. Folge, Bd. 34..

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.

ISBN: 9783319273716$q(electronic bk.)

Standard No.: 10.1007/978-3-319-27371-6doiSubjects--Topical Terms:

576824
Curves, Plane.

LC Class. No.: QA567

Dewey Class. No.: 516.352

Rigid geometry of curves and their Jacobians
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520 $a 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.
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