Rationally isotropic quadratic spaces are locally isotropic

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• Ivan Panin (St Petersburg)
• Wednesday 05 May 2010, 14:15-15:15
• MR13, CMS.

If you have a question about this talk, please contact Burt Totaro.

Let R be a semi-local regular integral domain containing a field of characteristic different from 2, and K its field of fractions. Assuming that all residue fields of R are infinite, we show that a quadratic form over R which becomes isotropic over K is isotropic over R. This solves a question raised by Colliot-Thelene. The proof is based on a moving lemma of Levine and Morel, on a recent improvement due to Gabber of the alteration theorem due to de Jong, and on a theorem due to the author and Rehmann. A previous result of the author concerned the characteristic zero case.

This talk is part of the Algebraic Geometry Seminar series.

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