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Event № 408

Event № 408
TE Algebra Seminar - Uriya First 02/01/2017, Monday, 12:30
Type: Seminar
Name: Algebra Seminar
Title: Semisimply degenerate quadratic forms and a conjecture of Grothendieck and Serre
Speaker: Uriya First
Place: Amado, 619, Technion
Abstract:

Abstract: Let R be a discrete valuation ring with fraction field K. It is a classical result that two nondegenerate quadratic forms over R that become isomorphic over K are already isomorphic over R. [Here, a quadratic form over R is a map q:R^n->R of the form q(x)=x^{T}Mx with M a symmetric matrix, and q is nondegenerate if M is invertible over R.] This result is a special case of a conjecture of Grothendieck and Serre concerning the etale cohomology of reductive group schemes over local regular rings. Much progress has been made recently in proving the conjecture, mostly due to Panin.I will discuss a generalization of the aforementioned result to certain degenerate quadratic and also to hermitian forms over certain (non-commutative) R-algebras. This generalization suggests that the conjecture of Grothedieck and Serre may apply to certain families of non-reductive groups arising from Bruhat-Tits theory. Certain cases of this extended conjecture were already verified and others are currently under investigation.

SubmittedBy: Shiri Kaplan-Shabat , mathsec@technion.ac.il
EventLink: Event № 408
Print event № 408 …
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