Abstract
We give a geometric description of the pair (V,p), where V is an algebraic variety over a non-trivially valued algebraically closed field K with valuation ring OK and p is a Zariski dense generically stable type concentrated on V, by defining a fully faithful functor to the category of schemes over OK with residual dominant morphisms over OK.Under this functor, the pair (an algebraic group, a generically stable generic type of a subgroup) gets sent to a group scheme over OK. This returns a geometric description of the subgroup as the set of OK-points of the group scheme, generalizing a previous result in the affine case.We also study a maximum modulus principle on schemes over OK and show that the schemes obtained by this functor enjoy it.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
