{"id":{"repo_id":"fu-berlin","oai_identifier":"oai:refubium.fu-berlin.de:fub188/31310"},"canonical_url":"https://search.dev.ndltd.org/etd/fu-berlin/oai:refubium.fu-berlin.de:fub188/31310","repository":{"repo_id":"fu-berlin","name":"Freie Universität Berlin","base_url":"https://refubium.fu-berlin.de/oai/request"},"display":{"title":"p-primary torsion part of Bloch's cycle complex from Grothendieck's coherent duality point of view","abstract":"Let X be a separated scheme of finite type over k with k being a perfect field of positive characteristic p. In this thesis we define a complex K_{n,X,log} via Grothendieck’s duality theory of coherent sheaves following [Kat87] and build up a quasi-isomorphism from the Kato-Moser complex of logarithmic de Rham-Witt sheaves \\tilde \\nu_{n,X} to K_{n,X,log} for the etale topology, and also for the Zariski topology under the extra assumption k =\\bar k. Combined with Zhong’s quasi-isomorphism from Bloch’s cycle complex Z^c_X to \\tilde \\nu_{n,X} [Zho14, 2.16], we deduce certain vanishing, etale descent properties as well as invariance under rational resolutions for higher Chow groups of 0-cycles with Z/p^n-coefficients.","abstract_html":"Let X be a separated scheme of finite type over k with k being a perfect field of positive characteristic p. In this thesis we define a complex K_{n,X,log} via Grothendieck’s duality theory of coherent sheaves following [Kat87] and build up a quasi-isomorphism from the Kato-Moser complex of logarithmic de Rham-Witt sheaves \\tilde \\nu_{n,X} to K_{n,X,log} for the etale topology, and also for the Zariski topology under the extra assumption k =\\bar k. Combined with Zhong’s quasi-isomorphism from Bloch’s cycle complex Z^c_X to \\tilde \\nu_{n,X} [Zho14, 2.16], we deduce certain vanishing, etale descent properties as well as invariance under rational resolutions for higher Chow groups of 0-cycles with Z/p^n-coefficients.","abstract_has_math":false,"creators":["Ren, Fei"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021","date_published":"2021","updated_at":"2026-08-21T16:44:52Z","subjects":["Higher Chow groups","Grothendieck duality theory","log forms"],"languages":["eng"],"rights":[],"rights_urls":["https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://dx.doi.org/10.17169/refubium-31046"],"render_values":[{"text":"http://dx.doi.org/10.17169/refubium-31046","href":"http://dx.doi.org/10.17169/refubium-31046","code":true}]}]},"links":{"outbound_url":"https://refubium.fu-berlin.de/handle/fub188/31310","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://refubium.fu-berlin.de/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Arefubium.fu-berlin.de%3Afub188%2F31310","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Ren, Fei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2021"]},{"key":"dc:type","label":"Dc Type","values":["doc-type:doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Higher Chow groups","Grothendieck duality theory","log forms"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights.uri","label":"Rights URI","values":["https://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://refubium.fu-berlin.de/handle/fub188/31310","http://dx.doi.org/10.17169/refubium-31046"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let X be a separated scheme of finite type over k with k being a perfect field of positive characteristic p. In this thesis we define a complex K_{n,X,log} via Grothendieck’s duality theory of coherent sheaves following [Kat87] and build up a quasi-isomorphism from the Kato-Moser complex of logarithmic de Rham-Witt sheaves \\tilde \\nu_{n,X} to K_{n,X,log} for the etale topology, and also for the Zariski topology under the extra assumption k =\\bar k. Combined with Zhong’s quasi-isomorphism from Bloch’s cycle complex Z^c_X to \\tilde \\nu_{n,X} [Zho14, 2.16], we deduce certain vanishing, etale descent properties as well as invariance under rational resolutions for higher Chow groups of 0-cycles with Z/p^n-coefficients."]},{"key":"dc:title","label":"Title","values":["p-primary torsion part of Bloch's cycle complex from Grothendieck's coherent duality point of view"]}]}],"canonical_facts":{"dc:creator":["Ren, Fei"],"dc:date.issued":["2021"],"dc:description.abstract":["Let X be a separated scheme of finite type over k with k being a perfect field of positive characteristic p. In this thesis we define a complex K_{n,X,log} via Grothendieck’s duality theory of coherent sheaves following [Kat87] and build up a quasi-isomorphism from the Kato-Moser complex of logarithmic de Rham-Witt sheaves \\tilde \\nu_{n,X} to K_{n,X,log} for the etale topology, and also for the Zariski topology under the extra assumption k =\\bar k. Combined with Zhong’s quasi-isomorphism from Bloch’s cycle complex Z^c_X to \\tilde \\nu_{n,X} [Zho14, 2.16], we deduce certain vanishing, etale descent properties as well as invariance under rational resolutions for higher Chow groups of 0-cycles with Z/p^n-coefficients."],"dc:identifier.uri":["https://refubium.fu-berlin.de/handle/fub188/31310","http://dx.doi.org/10.17169/refubium-31046"],"dc:language":["eng"],"dc:rights.uri":["https://creativecommons.org/licenses/by/4.0/"],"dc:subject":["Higher Chow groups","Grothendieck duality theory","log forms"],"dc:title":["p-primary torsion part of Bloch's cycle complex from Grothendieck's coherent duality point of view"],"dc:type":["doc-type:doctoralThesis"]},"updated_at":"2026-08-21T16:44:52Z"}