{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-1565"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-1565","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"On the Witt groups of schemes","abstract":"We consider two questions about the Witt groups of schemes: the first is the question of finite generation of the shifted Witt groups of a smooth variety over a finite field; the second is the Gersten conjecture. Regarding the first, we prove that the shifted Witt groups of curves and surfaces are finite, and that finite generation of the motivic cohomology groups with mod 2 coefficients implies finite generation of the Witt groups. Regarding the second, we prove the Gersten conjecture for the Witt groups in the case of a local ring that is essentially smooth over a discrete valuation ring (DVR) having infinite residue field. We deduce from this the case of a local ring that is regular over such a DVR.","abstract_html":"We consider two questions about the Witt groups of schemes: the first is the question of finite generation of the shifted Witt groups of a smooth variety over a finite field; the second is the Gersten conjecture. Regarding the first, we prove that the shifted Witt groups of curves and surfaces are finite, and that finite generation of the motivic cohomology groups with mod 2 coefficients implies finite generation of the Witt groups. Regarding the second, we prove the Gersten conjecture for the Witt groups in the case of a local ring that is essentially smooth over a discrete valuation ring (DVR) having infinite residue field. We deduce from this the case of a local ring that is regular over such a DVR.","abstract_has_math":false,"creators":["Jacobson, Jeremy Allen"],"institution":"Mathematics","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Applied Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-01-01T08:00:00Z","date_published":"2012-01-01T08:00:00Z","updated_at":"2026-07-24T02:57:49Z","subjects":["quadratic forms","Gersten conjecture","finite generation"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-07092012-113356","https://repository.lsu.edu/gradschool_dissertations/566"],"render_values":[{"text":"etd-07092012-113356","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/566","href":"https://repository.lsu.edu/gradschool_dissertations/566","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.566","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Jacobson, Jeremy Allen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-05-16"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:09:15Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["quadratic forms","Gersten conjecture","finite generation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-07092012-113356","10.31390/gradschool_dissertations.566","https://repository.lsu.edu/gradschool_dissertations/566"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We consider two questions about the Witt groups of schemes: the first is the question of finite generation of the shifted Witt groups of a smooth variety over a finite field; the second is the Gersten conjecture. Regarding the first, we prove that the shifted Witt groups of curves and surfaces are finite, and that finite generation of the motivic cohomology groups with mod 2 coefficients implies finite generation of the Witt groups. Regarding the second, we prove the Gersten conjecture for the Witt groups in the case of a local ring that is essentially smooth over a discrete valuation ring (DVR) having infinite residue field. We deduce from this the case of a local ring that is regular over such a DVR."]},{"key":"dc:title","label":"Title","values":["On the Witt groups of schemes"]}]}],"canonical_facts":{"dc:creator":["Jacobson, Jeremy Allen"],"dc:date":["2012-05-16"],"dc:date.available":["2022-05-12T23:09:15Z"],"dc:description.abstract":["We consider two questions about the Witt groups of schemes: the first is the question of finite generation of the shifted Witt groups of a smooth variety over a finite field; the second is the Gersten conjecture. Regarding the first, we prove that the shifted Witt groups of curves and surfaces are finite, and that finite generation of the motivic cohomology groups with mod 2 coefficients implies finite generation of the Witt groups. Regarding the second, we prove the Gersten conjecture for the Witt groups in the case of a local ring that is essentially smooth over a discrete valuation ring (DVR) having infinite residue field. We deduce from this the case of a local ring that is regular over such a DVR."],"dc:identifier":["etd-07092012-113356","10.31390/gradschool_dissertations.566","https://repository.lsu.edu/gradschool_dissertations/566"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["quadratic forms","Gersten conjecture","finite generation"],"dc:title":["On the Witt groups of schemes"],"thesis:degree_discipline":["Applied Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Mathematics"]},"updated_at":"2026-07-24T02:57:49Z"}