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Cohomological Invariants of Quadratic Forms

Thesis advisor: Benjamin V. Howard / Given a field <italic>F</italic>, an algebraic closure <italic>K</italic> and an <italic>F</italic>-vector space <italic>V</italic>, we can tensor the space <italic>V</italic> with the algebraic closure <italic>K</italic>. Two quadratic spaces of the same dimension become isomorphic when tensored with an algebraic closure. The failure of this isomorphism over <italic>F</italic> is measured by the Hasse invariant. This paper explains how the determinants and Hasse Invariants of quadratic forms are related to certain cohomology classes constructed from specific short exact sequences. In particular, the Hasse Invariant is defined as an element of the Brauer group. / Thesis (MA) — Boston College, 2010. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

Identiferoai:union.ndltd.org:BOSTON/oai:dlib.bc.edu:bc-ir_101504
Date January 2010
CreatorsHarvey, Ebony Ann
PublisherBoston College
Source SetsBoston College
LanguageEnglish
Detected LanguageEnglish
TypeText, thesis
Formatelectronic, application/pdf
RightsCopyright is held by the author, with all rights reserved, unless otherwise noted.

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