On an isotropy criterion for quadratic forms over function fields of curves over non-dyadic complete discrete valuation rings

@article{DavidGrimm2016,
abstract = {Harbater, Hartmann and Krashen obtained in 2015 a criterion for the existence of rational points on projective (or principal) homogeneous varieties for rational connected algebraic groups defined over function fields of normal curves over a complete discrete valuation ring in terms of completions of local rings at special points. This was obtained by a reduction via Artin approximation to a related patching problem solved by the same authors in 2009. In the special case of projective quadrics, we present a more elementary reduction in the non-dyadic case. The proof is strongly inspired by the proof of a more Hasse-like local-global principle due to Colliot-Thélène, Parimala and Suresh, and we present a variant of their proof based on the mentioned criterion.},
author = {David Grimm},
journal = {Banach Center Publications},
keywords = {discrete valuation rings; isotropy; quadratic forms; function fields},
language = {eng},
number = {1},
pages = {95-103},
title = {On an isotropy criterion for quadratic forms over function fields of curves over non-dyadic complete discrete valuation rings},
url = {http://eudml.org/doc/286434},
volume = {108},
year = {2016},
}

TY - JOUR
AU - David Grimm
TI - On an isotropy criterion for quadratic forms over function fields of curves over non-dyadic complete discrete valuation rings
JO - Banach Center Publications
PY - 2016
VL - 108
IS - 1
SP - 95
EP - 103
AB - Harbater, Hartmann and Krashen obtained in 2015 a criterion for the existence of rational points on projective (or principal) homogeneous varieties for rational connected algebraic groups defined over function fields of normal curves over a complete discrete valuation ring in terms of completions of local rings at special points. This was obtained by a reduction via Artin approximation to a related patching problem solved by the same authors in 2009. In the special case of projective quadrics, we present a more elementary reduction in the non-dyadic case. The proof is strongly inspired by the proof of a more Hasse-like local-global principle due to Colliot-Thélène, Parimala and Suresh, and we present a variant of their proof based on the mentioned criterion.
LA - eng
KW - discrete valuation rings; isotropy; quadratic forms; function fields
UR - http://eudml.org/doc/286434
ER -