Equivalence relations of quadratic forms in characteristic 2 and quasilinear p-forms

Zemkova, Kristyna

Equivalence relations of quadratic forms in characteristic 2 and quasilinear p-forms

dc.contributor.advisor	Hoffmann, Detlev
dc.contributor.author	Zemkova, Kristyna
dc.contributor.referee	Unger, Thomas
dc.date.accepted	2022-12-07
dc.date.accessioned	2022-12-14T07:10:39Z
dc.date.available	2022-12-14T07:10:39Z
dc.date.issued	2022
dc.description.abstract	This thesis deals with quadratic forms and quasilinear p-forms in positive characteristic. In this setting, there are three well-known equivalence relations -- similarity, birational equivalence, and stable birational equivalence. Inspired by an algebraic characterization of motivic equivalence of quadratic forms over fields of characteristic other than two, this thesis defines a new equivalence relation -- the Vishik equivalence. The thesis is divided into chapters based on the kind of forms treated: quasilinear p-forms (over fields of characteristic p), totally singular quadratic forms, nonsingular quadratic forms, and singular quadratic forms (all of them over fields of characteristic 2). The main goal is to compare the four above-mentioned equivalences for each of those kinds of forms. We also derive some consequences of two forms being equivalent for each of the four equivalences separately. In particular, we give a new characterization of the stable birational equivalence for quadratic forms. Moreover, we provide some new results regarding the isotropy of quasilinear p-forms over field extensions.	en
dc.identifier.uri	http://hdl.handle.net/2003/41163
dc.identifier.uri	http://dx.doi.org/10.17877/DE290R-23010
dc.language.iso	en	de
dc.subject	Quadratic forms	en
dc.subject	Quasilinear p-forms	en
dc.subject	Finite characteristic	en
dc.subject	Equivalence relations	en
dc.subject	Quadrics	en
dc.subject.ddc	510
dc.subject.rswk	Quadratische Form	de
dc.subject.rswk	Äquivalenzrelation	de
dc.subject.rswk	p-Form	de
dc.subject.rswk	Quadrik	de
dc.title	Equivalence relations of quadratic forms in characteristic 2 and quasilinear p-forms	en
dc.type	Text	de
dc.type.publicationtype	doctoralThesis	de
dcterms.accessRights	open access
eldorado.secondarypublication	false	de

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Lehrstuhl VI Algebra und Geometrie