By Werner Lütkebohmert (auth.)

ISBN-10: 3319273698

ISBN-13: 9783319273693

ISBN-10: 331927371X

ISBN-13: 9783319273716

This booklet offers probably the most vital elements of inflexible geometry, particularly its purposes to the learn of soft algebraic curves, in their Jacobians, and of abelian kinds - them all outlined over a whole non-archimedean valued box. The textual content starts off with a survey of the root of inflexible geometry, after which makes a speciality of an in depth remedy of the purposes. on the subject of curves with cut up rational aid there's a entire analogue to the attention-grabbing thought of Riemann surfaces. in terms of right delicate staff kinds the uniformization and the development of abelian types are handled intimately.

Rigid geometry was once proven by means of John Tate and used to be enriched by means of a proper algebraic technique introduced by means of Michel Raynaud. It has proved as a way to demonstrate the geometric principles at the back of the summary tools of formal algebraic geometry as utilized by Mumford and Faltings. This ebook can be of serious use to scholars wishing to go into this box, in addition to these already operating in it.