Rigid Analytic Geometry and Its Applications

Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.

Inhalt

Preface Valued fields and normed spaces The projective line Affinoid algebras Rigid spaces Curves and their reductions Abelian varieties Points of rigid spaces, rigid cohomology Etale cohomology of rigid spaces Covers of algebraic curves References List of Notation Index