In the context of non-archimedean analytic geometry, affinoid domains are basic model spaces: a Berkovich analytic space is, in particular, a topological space equipped with an atlas by (analytic spectra underlying) affinoid domains.
An affinoid domain in an affinoid space is a closed subset such that there is a homomorphism of -affinoid spaces
for some , whose image is , and such that every other morphism of -affinoid spaces into whose image is contained in uniquely factors through this morphism.
A morphism of affinoid spaces is an affionoid domain embedding if it induces an isomorphism of with an affinoid domain in
These are the “admissible morphisms” in the site of affinoid domains. (…)
Vladimir Berkovich, section 2.2 of Non-archimedean analytic spaces, lectures at the Advanced School on -adic Analysis and Applications, ICTP, Trieste, 31 August - 11 September 2009 (pdf)
Doosung Park, Affinoid domains, lecture notes (pdf)
Last revised on July 17, 2014 at 23:09:15. See the history of this page for a list of all contributions to it.