Formal and rigid geometry. I: Rigid spaces. (English) Zbl 0808.14017

Bosch, Siegfried; Lütkebohmert, Werner

Math. Ann. 295, No. 2, 291-317 (1993).

Rigid geometry can be approached in two different ways. A first approach is via analytic techniques. A second method is to view rigid spaces in the framework of formal schemes.
The authors explain this latter method in a general situation. In the classical rigid case the base is a valuation ring of Krull dimension 1. Here the base \(R\) is allowed to be a noetherian ring which is complete with respect to the \({\mathcal I}\)-adic topology for some ideal \({\mathcal I} \subset R\). The basic results and constructions concerning admissible formal schemes are given. Then the correspondence between admissible formal schemes and rigid analytical spaces is explained. In a final section the authors extend their approach to M. Raynaud’s relative rigid spaces over a global noetherian ring.

Reviewer: G.van Steen (Antwerpen)

MSC:

14G20	Local ground fields in algebraic geometry
11G25	Varieties over finite and local fields

Keywords:

formal schemes; rigid analytical spaces

Citations:

Zbl 0808.14018

References:

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