2026-09-20T09:36:57Zhttps://digital.lib.washington.edu/server/oai/request

oai:digital.lib.washington.edu:1773/443742026-02-15T22:34:52Zcom_1773_4888col_1773_4939

Lieblich, Max Dorfsman-Hopkins, Gabriel David 2019-08-14T22:36:19Z 2019-08-14T22:36:19Z 2019-08-14 2019 DorfsmanHopkins_washington_0250E_20133.pdf http://hdl.handle.net/1773/44374 Thesis (Ph.D.)--University of Washington, 2019 To understand the structure of an algebraic variety we often embed it in various projective spaces. This develops the notion of projective geometry which has been an invaluable tool in algebraic geometry. 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. 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. application/pdf en_US CC BY-SA Algebraic Geometry Commutative Algebra Number Theory Mathematics Mathematics Projective Geometry for Perfectoid Spaces Thesis Open Access open.access