Type of Document Dissertation Author Jacobson, Jeremy Allen Author's Email Address email@example.com URN etd-07092012-113356 Title On the Witt Groups of Schemes Degree Doctor of Philosophy (Ph.D.) Department Mathematics Advisory Committee
Advisor Name Title Schlichting, Marco Committee Chair Achar, Pramod Committee Member Hoffman, Jerome Committee Member Perlis, Robert Committee Member Ricks, Thomas Dean's Representative Keywords
- quadratic forms
- Gersten conjecture
- finite generation
Date of Defense 2012-05-16 Availability unrestricted AbstractWe 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.
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