# Rationally isomorphic quadratic objects

Seminar

Speaker

Dr. Uriya First (University of British Columbia)

Date

15/04/2015 - 11:30 - 10:30Add to Calendar

`2015-04-15 10:30:00``2015-04-15 11:30:00``Rationally isomorphic quadratic objects``Let R be a discrete valuation ring with fraction field F. Two algebraic objects (say, quadratic forms) defined over R are said to be rationally isomorphic if they become isomorphic after extending scalars to F. In the case of unimodular quadratic forms, it is a classical result that rational isomorphism is equivalent to isomorphism. This has been recently extended to "almost umimodular" forms by Auel, Parimala and Suresh. I will present further generalizations to hermitian forms over (certain) involutary R-algebras and quadratic spaces equipped with a group action ("G-forms"). The results can be regarded as versions of the Grothendieck-Serre conjecture for certain non-reductive groups. (Joint work with Eva Bayer-Fluckiger.)``Third floor seminar room``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room

Abstract

Let R be a discrete valuation ring with fraction field F. Two algebraic objects (say, quadratic forms) defined over R are said to be rationally isomorphic if they become isomorphic after extending scalars to F. In the case of unimodular quadratic forms, it is a classical result that rational isomorphism is equivalent to isomorphism. This has been recently extended to "almost umimodular" forms by Auel, Parimala and Suresh. I will present further generalizations to hermitian forms over (certain) involutary R-algebras and quadratic spaces equipped with a group action ("G-forms"). The results can be regarded as versions of the Grothendieck-Serre conjecture for certain

*non-reductive*groups.(Joint work with Eva Bayer-Fluckiger.)

Last Updated Date : 08/04/2015