TY  - BOOK
AU  - Lutkebohmert,Werner
TI  - Rigid geometry of curves and their jacobians
T2  - Ergebnisse der mathematik und ihrer grenzgebiete, 3. folge 
SN  - 9783319273693 (hardcover : alk. paper)
U1  - 516.35 23
PY  - 2016///
CY  - Cham :    
PB  - Springer
KW  - Plane curves
KW  - Jacobians
N1  - Includes bibliographical references and index; 1. Classical rigid geometry --
2. Mumford curves --
3. Formal and rigid geometry --
4. Rigid analytic curves --
5. Jacobian varieties --
6. Raynaud extensions --
7. Abeloid varieties --
Appendix --
Glossary of notations --
References --
Index
N2  - 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
ER  -