Étale Cohomology of Rigid Analytic Varieties and Adic Spaces

Softcover Nachdruck of the original 1. Auflage 1996
ISBN: 978-3-663-09992-5
Verlag: Vieweg+Teubner Verlag

Buch, Englisch, Deutsch, Band 30, 450 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 794 g

Reihe: Aspects of Mathematics

Tate introduced analytic spaces over non-archimedean fields which are called rigid analytic varieties ([T]). Raynaud realized that the category of quasi-compact quasi­ separated rigid analytic varieties over a non-archimedean field k is equivalent to the localization of the category of formal schemes of finite type over the valuation 0 ring k of k with respect to the class of admissible formal blowing-ups ([RI]). This approach to rigid analytic geometry can be extended by localizing a more general class of formal schemes with respect to admissible formal blowing-ups. The result­ ing category is called the category of relative rigid spaces ([BL]). But one can also extend Tate's definition of analytic spaces. We call this more general analytic spaces analytic adic spaces ([Hu]). The category of analytic adic spaces is a full subcategory of the category of locally and topologically ringed spaces with a distinguished valu­ ation on every residue field of the structure sheaf. There is a naturally fully faithful functor d from the category of relative rigid spaces to the category of analytic adic spaces. The aim of this text is to develop basic properties of the etale cohomology of torsion sheaves on analytic adic spaces: base change theorems, Poincare duality, finiteness, comparison theorems. For a rigid analytic variety X, or more general relative rigid space X, the etale topos Xd of X is naturally equivalent to the etale topos d(X)it of the analytic adic space d(X) associated with X.

Zielgruppe

Graduate

Autoren/Hrsg.

Huber, Roland

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

Étale cohomology of rigid analytic varieties (summary).- 1 Adic spaces.- 2 The étale site of a rigid analytic variety and an adic space.- 3 Comparison theorems.- 4 Base change theorems.- 5 Cohomology with compact support.- 6 Finiteness.- 7 Poincaré Duality.- 8 Partially proper sites of rigid analytic varieties and adic spaces.- A Appendix.- Index of notations.- Index of terminology.

Über Autor(innen)

Prof. Dr. Roland Huber is Professor of Mathematics at the Department of Mathematics and Informatics in the School of Mathematics and Natural Sciences of the University of Wuppertal, Germany.