MATH Seminar

Title: Unitary descent properties
Seminar: Algebra
Speaker: Eva Bayer of Swiss Federal Institute of Technology, Lausanne (EPFL)
Contact: R. Parimala, parimala@mathcs.emory.edu
Date: 2009-12-07 at 4:00PM
Venue: W306
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Abstract: Let $k$ be a field of characteristic $\not = 2$, let $L/k$ be an odd degree extension and let $U$ be a unitary group defined over $k$. It is well--known that the natural map $H^1(k,U) \to H^1(L,U)$ is injective. Suppose that $L/k$ is Galois with group $G$. Is then $H^1(k,U) \to H^1(L,U)^G$ a bijection? This is true for orthogonal groups, and one of the main ingredients in the proof is a result of Rosenberg and Ware concerning a descent property for Witt rings of quadratic forms, namely that $W(L)^G \simeq W(k)$. This talk will present a generalization of the Rosenberg--Ware theorem to Witt groups of hermitian forms, as well as some applications of this result, in particular to the above mentioned Galois cohomology descent question.