Uniformly rigid spaces

Kappen, Christian

doi:10.2140/ant.2012.6.341

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Uniformly rigid spaces

Christian Kappen

Vol. 6 (2012), No. 2, 341–388

DOI: 10.2140/ant.2012.6.341

Abstract

We define a new category of nonarchimedean analytic spaces over a complete discretely valued field, which we call uniformly rigid. It extends the category of rigid spaces, and it can be described in terms of bounded functions on products of open and closed polydiscs. We relate uniformly rigid spaces to their associated classical rigid spaces, and we transfer various constructions and results from rigid geometry to the uniformly rigid setting. In particular, we prove an analog of Kiehl’s patching theorem for coherent ideals, and we define the uniformly rigid generic fiber of a formal scheme of formally finite type. This uniformly rigid generic fiber is more intimately linked to its model than the classical rigid generic fiber obtained via Berthelot’s construction.

Keywords

semiaffinoid, uniformly rigid, formally finite type, rigid geometry, formal geometry, Berthelot construction

Mathematical Subject Classification 2010

Primary: 14G22

Secondary: 14K15

Milestones

Received: 6 September 2010

Revised: 22 February 2011

Accepted: 25 March 2011

Published: 24 June 2012

Authors

Christian Kappen
Institut für Experimentelle Mathematik Universität Duisburg-Essen Ellernstrasse 29 D-45326 Essen Germany
http://esaga.uni-due.de/christian.kappen

Vol. 6, No. 2, 2012