{"id":{"repo_id":"washington","oai_identifier":"oai:digital.lib.washington.edu:1773/44374"},"canonical_url":"https://search.dev.ndltd.org/etd/washington/oai:digital.lib.washington.edu:1773/44374","repository":{"repo_id":"washington","name":"University of Washington","base_url":"https://digital.lib.washington.edu/server/oai/request"},"display":{"title":"Projective Geometry for Perfectoid Spaces","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Dorfsman-Hopkins, Gabriel David"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Lieblich, Max"],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-08-14","date_published":"2019-08-14","updated_at":"2026-07-24T05:58:10Z","subjects":["Algebraic Geometry","Commutative Algebra","Number Theory","Mathematics"],"languages":["en_US"],"rights":["CC BY-SA"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1773/44374","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Lieblich, Max"]},{"key":"dc:creator","label":"Author","values":["Dorfsman-Hopkins, Gabriel David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-08-14T22:36:19Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2019-08-14T22:36:19Z"]},{"key":"dc:date.issued","label":"Date","values":["2019-08-14"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic Geometry","Commutative Algebra","Number Theory","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["CC BY-SA"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["DorfsmanHopkins_washington_0250E_20133.pdf"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1773/44374"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph.D.)--University of Washington, 2019"]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Projective Geometry for Perfectoid Spaces"]}]}],"canonical_facts":{"dc:contributor.advisor":["Lieblich, Max"],"dc:creator":["Dorfsman-Hopkins, Gabriel David"],"dc:date.accessioned":["2019-08-14T22:36:19Z"],"dc:date.available":["2019-08-14T22:36:19Z"],"dc:date.issued":["2019-08-14"],"dc:description":["Thesis (Ph.D.)--University of Washington, 2019"],"dc:description.abstract":["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."],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["DorfsmanHopkins_washington_0250E_20133.pdf"],"dc:identifier.uri":["http://hdl.handle.net/1773/44374"],"dc:language.iso":["en_US"],"dc:rights":["CC BY-SA"],"dc:subject":["Algebraic Geometry","Commutative Algebra","Number Theory","Mathematics"],"dc:title":["Projective Geometry for Perfectoid Spaces"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T05:58:10Z"}