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SUMMARY:Rationally isotropic quadratic spaces are locally isotropic - Ivan
  Panin (St Petersburg)
DTSTART:20100505T131500Z
DTEND:20100505T141500Z
UID:TALK22921@talks.cam.ac.uk
CONTACT:Burt Totaro
DESCRIPTION:Let R be a semi-local regular integral domain containing a fie
 ld of characteristic different from 2\, and K its field of fractions. Assu
 ming 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 solve
 s a question raised by Colliot-Thelene. The proof is based on a moving lem
 ma of Levine and Morel\, on a recent improvement due to Gabber of the alte
 ration theorem due to de Jong\, and on a theorem due to the author and Reh
 mann. A previous result of the author concerned the characteristic zero ca
 se.
LOCATION:MR13\, CMS
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