Principe local global pour les espaces lin\'eaires sur les intersections de deux quadriques

TL;DR

This paper offers an alternative proof for the local-global principle concerning the existence of linear spaces within smooth complete intersections of two quadrics, extending prior results in algebraic geometry.

Contribution

It provides a new proof approach for a more general theorem on linear spaces on intersections of quadrics, building on previous work by Jahnel and Loughran.

Findings

Alternative proof of the local-global principle

Extension to more general cases of intersections of quadrics

Validation of the principle in broader settings

Abstract

In arXiv:1410.5671, Jahnel and Loughran prove the local global principle for existence of linear spaces of dimension $r$ on smooth complete intersections of two quadrics in projective space of dimension $2r+2$. We present an alternative proof of a slightly more general result. ----- Dans arXiv:1410.5671, Jahnel et Loughran \'etablissent un principe local-global pour l'existence d'espaces lin\'eaires de dimension $r$ dans les intersections compl\`etes lisses de deux quadriques dans un espace projectif de dimension $2r+2$. On donne une d\'emonstration alternative d'un r\'esultat un peu plus g\'en\'eral.