Detailansicht
Rigid Geometry of Curves and Their Jacobians
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 61
ISBN/EAN: 9783319273693
Umbreit-Nr.: 8827954
Sprache:
Englisch
Umfang: xviii, 386 S., 1 s/w Illustr., 386 p. 1 illus.
Format in cm:
Einband:
gebundenes Buch
Erschienen am 03.02.2016
Auflage: 1/2016
- Zusatztext
- 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.
- Kurztext
- The first comprehensive presentation of the whole topic of curves, Jacobians, abelian varieties and proper analytic group varieties over non-archimedian fieldsIntroduces the powerful tools of formal algebraic geometry as used in arithmetic geometryThe book builds a bridge to the more advanced research on the moduli of degeneration of abelian varieties which is a central object in arithmetic geometryIncludes supplementary material: sn.pub/extras