MathCS Seminar

Title: Involutions, odd degree extensions and generic splitting
Seminar: Algebra
Speaker: Anne Queguiner-Mathieuem of Universite Paris
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-03-26 at 3:00PM
Venue: W303
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Abstract:
Let $q$ be a quadratic form over a field $F$, and let $L$ be an odd-degree field extension of $F$. A classical theorem, known as Springer's theorem, asserts that if $q$ is isotropic (resp. hyperbolic) after scalar extension to $L$, it actually is isotropic (resp. hyperbolic) over the base field. One may ask whether a similar result holds for algebras with involution. In the talk, we will survey known results on this question, and explain the relation with the study of isotropy and hyperbolicity over some relevant function fields. New low degree results will also be included.

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