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

• Autorzy: David Grimm
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 20G35: Linear algebraic groups over ad\`eles and other rings and schemes
• 11G99: None of the above, but in this section
• 11E12: Quadratic forms over global rings and fields
• 14G05: Rational points
• 14G99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2016
• Tom: 108
• Numer: 1
• Strony: 95-103

Daty

wydano

2016

Twórcy

autor

David Grimm

• Departamento de Matemáticas, Facultad de Ciencia, Universidad de Santiago de Chile, Av. Libertador Bernardo O'Higgins 3363, Santiago, Chile

Identyfikatory

DOI

10.4064/bc108-0-8