Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

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

100%

Grimm D.

Banach Center Publications

2016

tom 108

nr 1

95-103

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.

Ograniczanie wyników

1 Banach Center Publications

1 Grimm D.

1 2016

Wyniki wyszukiwania

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