Titelaufnahme
Titelaufnahme
- TitelProjective geometry for perfectoid spaces
- Verfasser
- Enthalten inMünster Journal of Mathematics, H. Münster Journal of Mathematics, S. 445-484
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- SpracheEnglisch
- DokumenttypAufsatz in einer Zeitschrift
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Zusammenfassung
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.
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