Title page for ETD etd-07092012-113356


Type of Document Dissertation
Author Jacobson, Jeremy Allen
Author's Email Address jjaco19@math.lsu.edu
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
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.

Files
  Filename       Size       Approximate Download Time (Hours:Minutes:Seconds) 
 
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  CatalogingAbstract.pdf 25.85 Kb 00:00:07 00:00:03 00:00:03 00:00:01 < 00:00:01
  DissertationJacobson.pdf 671.24 Kb 00:03:06 00:01:35 00:01:23 00:00:41 00:00:03

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