Quadratic points on intersections of two quadrics

Abstract

We prove that a smooth complete intersection of two quadrics of dimension at least $2$ over a number field has index dividing $2$, i.e., that it possesses a rational $0$-cycle of degree $2$.

arXiv comment39 pages. Section on local fields moved to S2 (prev. S4), and added background on quadratic forms over char 2 fields and more details on Tian's semistable models. Added Cor. 2.7, which simplifies the local fields proof, and added a different proof specifically for local and global fields of char. 2. Clarified proof of Prop. 3.6 (prev. Prop. 2.6). To appear in Algebra and Number Theory

References in corpus (5)

• Algebraic families of nonzero elements of Shafarevich-Tate groups
• Intersections de deux quadriques et pinceaux de courbes de genre 1
• Hasse principle for three classes of varieties over global function fields
• Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2
• The period-index problem in WC-groups II: abelian varieties

Cited by in corpus (4)

• Retour sur l'arithmétique des intersections de deux quadriques, avec un appendice par A. Kuznestov
• The Brauer-Manin obstruction for nonisotrivial curves over global function fields
• Quartic del Pezzo surfaces without quadratic points
• Arithmetic of Châtelet surface bundles revisited