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Burnside form rings and the K-theory of forms
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Madden, Dylan (2021) Burnside form rings and the K-theory of forms. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3728850
Abstract
The Burnside form ring Z is the initial object and tensor unit in the category of form rings; therefore, its Grothendieck-Witt ring GW0(Z), since it acts on GWi(R; ) for any i ≥ 0 and any form ring (R; A), is of fundamental importance in the study of the K-theory of forms. We show that GW0(Z) is isomorphic to Z3 as an abelian group, and also give its ring structure.
Using an extension of scalars construction defined by a universal property, one can define a Burnside form ring R for any commutative ring R. After calculating GW0(Z), the remainder of the thesis calculates GW0(R) when R is a finite field. Along the way, we calculate GW0(R) for any ring R with 2 invertible and finitely generated projective R-modules free, and we define a determinant map which generalises the classical determinant map on symmetric bilinear forms.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | K-theory, Rings (Algebra) | ||||
Official Date: | June 2021 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Schlichting, Marco | ||||
Format of File: | |||||
Extent: | vi, 101 leaves | ||||
Language: | eng |
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