On the Witt groups of schemes

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.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2012

Author dc:creator

• Jacobson, Jeremy Allen

• quadratic forms
• Gersten conjecture
• finite generation

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-07092012-113356
https://repository.lsu.edu/gradschool_dissertations/566

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1565