Overconvergent subanalytic subsets in the framework of Berkovich spaces
Florent Martin
Universität Regensburg, Germany
![Overconvergent subanalytic subsets in the framework of Berkovich spaces cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-18-issue-10.png&w=3840&q=90)
Abstract
We study the class of overconvergent subanalytic subsets of a -affinoid space when is a non-archimedean field. These are the images along the projection of subsets defined with inequalities between functions of which are overconvergent in the variables of . In particular, we study the local nature, with respect to , of overconvergent subanalytic subsets. We show that they behave well with respect to the Berkovich topology, but not to the -topology. This gives counter-examples to previous results on the subject, and a way to correct them. Moreover, we study the case dim, for which a simpler characterisation of overconvergent subanalytic subsets is proven.
Cite this article
Florent Martin, Overconvergent subanalytic subsets in the framework of Berkovich spaces. J. Eur. Math. Soc. 18 (2016), no. 10, pp. 2405–2457
DOI 10.4171/JEMS/643