Uniformly rigid spaces
Abstract
We define a new category of non-archimedean 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.
Cite
@article{arxiv.1009.1056,
title = {Uniformly rigid spaces},
author = {Christian Kappen},
journal= {arXiv preprint arXiv:1009.1056},
year = {2011}
}
Comments
46 pages; typos corrected, terminology changed ("semi-affinoid pre-subdomains" -> "representable subsets", "semi-affinoid subspaces" -> "open semi-affinoid subspaces"), proof of Cor. 2.15 (formerly 2.14) rewritten, included proof that the urig G-top is finer than the Zar-top (Prop. 2.39), added proofs in Section 4, arguments in some proofs explained in greater detail, to appear in ANT