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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Rationally isotropic quadratic spaces are locally
isotropic - Ivan Panin (St Petersburg)
DTSTART;TZID=Europe/London:20100505T141500
DTEND;TZID=Europe/London:20100505T151500
UID:TALK22921AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/22921
DESCRIPTION:Let R be a semi-local regular integral domain cont
aining 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 rai
sed by Colliot-Thelene. The proof is based on a mo
ving lemma of Levine and Morel\, on a recent impro
vement due to Gabber of the alteration theorem due
to de Jong\, and on a theorem due to the author a
nd Rehmann. A previous result of the author concer
ned the characteristic zero case.
LOCATION:MR13\, CMS
CONTACT:Burt Totaro
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