{"id":{"repo_id":"oregon","oai_identifier":"oai:scholarsbank.uoregon.edu:1794/13244"},"canonical_url":"https://search.dev.ndltd.org/etd/oregon/oai:scholarsbank.uoregon.edu:1794/13244","repository":{"repo_id":"oregon","name":"University of Oregon","base_url":"https://scholarsbank.uoregon.edu/server/oai/request"},"display":{"title":"Chern Character for Global Matrix Factorizations","abstract":"We give a formula for the Chern character on the DG category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\\in \\Gamma(\\O_X)$. Our formula takes values in a Cech model for Hochschild homology. Our methods may also be adapted to get an explicit formula for the Chern character for perfect complexes of sheaves on $X$ taking values in right derived global sections of the De-Rham algebra. Along the way we prove that the DG version of the Chern Character coincides with the classical one for perfect complexes.","abstract_html":"We give a formula for the Chern character on the DG category of global matrix factorizations on a smooth scheme $X$ with superpotential <span class=\"etd-inline-math\">w\\in \\Gamma(\\O<sub>X</sub>)</span>. Our formula takes values in a Cech model for Hochschild homology. Our methods may also be adapted to get an explicit formula for the Chern character for perfect complexes of sheaves on $X$ taking values in right derived global sections of the De-Rham algebra. Along the way we prove that the DG version of the Chern Character coincides with the classical one for perfect complexes.","abstract_has_math":true,"creators":["Platt, David"],"institution":"University of Oregon","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":"Department of Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Polishchuk, Alexander"],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-10-03","date_published":"2013-10-03","updated_at":"2026-08-21T16:47:20Z","subjects":["Chern Character","Matrix Factorizations","Noncommutative Geometry"],"languages":["en_US"],"rights":["All Rights Reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1794/13244","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://scholarsbank.uoregon.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ascholarsbank.uoregon.edu%3A1794%2F13244","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Polishchuk, Alexander"]},{"key":"dc:creator","label":"Author","values":["Platt, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-10-03T23:32:01Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-10-03T23:32:01Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-10-03"]},{"key":"dc:publisher","label":"Institution","values":["University of Oregon"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Oregon"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Chern Character","Matrix Factorizations","Noncommutative Geometry"]}]},{"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":["All Rights Reserved."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1794/13244"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We give a formula for the Chern character on the DG category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\\in \\Gamma(\\O_X)$. Our formula takes values in a Cech model for Hochschild homology. Our methods may also be adapted to get an explicit formula for the Chern character for perfect complexes of sheaves on $X$ taking values in right derived global sections of the De-Rham algebra. Along the way we prove that the DG version of the Chern Character coincides with the classical one for perfect complexes."]},{"key":"dc:title","label":"Title","values":["Chern Character for Global Matrix Factorizations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Polishchuk, Alexander"],"dc:creator":["Platt, David"],"dc:date.accessioned":["2013-10-03T23:32:01Z"],"dc:date.available":["2013-10-03T23:32:01Z"],"dc:date.issued":["2013-10-03"],"dc:description.abstract":["We give a formula for the Chern character on the DG category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\\in \\Gamma(\\O_X)$. Our formula takes values in a Cech model for Hochschild homology. Our methods may also be adapted to get an explicit formula for the Chern character for perfect complexes of sheaves on $X$ taking values in right derived global sections of the De-Rham algebra. Along the way we prove that the DG version of the Chern Character coincides with the classical one for perfect complexes."],"dc:identifier.uri":["https://hdl.handle.net/1794/13244"],"dc:language.iso":["en_US"],"dc:publisher":["University of Oregon"],"dc:rights":["All Rights Reserved."],"dc:subject":["Chern Character","Matrix Factorizations","Noncommutative Geometry"],"dc:title":["Chern Character for Global Matrix Factorizations"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Department of Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Oregon"]},"updated_at":"2026-08-21T16:47:20Z"}