We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Projective geometry for perfectoid spaces.
- Authors
Dorfsman-Hopkins, Gabriel
- Abstract
We develop a perfectoid analog of projective geometry and explore how equipping a perfectoid space with a map to a certain analog of projective space can be a powerful tool to understand its geometric and arithmetic structure. In particular, we show that maps from a perfectoid space X to the perfectoid analog of projective space correspond to line bundles on X together with some extra data, reflecting the classical theory. We then use this notion to compare the Picard group of a perfectoid space and its tilt. Along the way, we give a complete classification of vector bundles on the perfectoid unit disk and compute the Picard group of the perfectoid analog of projective space.
- Subjects
PICARD groups; COMMERCIAL space ventures; VECTOR bundles; ARITHMETIC; PROJECTIVE spaces; PROJECTIVE geometry
- Publication
Münster Journal of Mathematics, 2021, Vol 14, Issue 2, p445
- ISSN
1867-5778
- Publication type
Article
- DOI
10.17879/06089644766