Quadratic points on intersections of two quadrics
Number Theory
2023-08-30 v4 Algebraic Geometry
Abstract
We prove that a smooth complete intersection of two quadrics of dimension at least over a number field has index dividing , i.e., that it possesses a rational -cycle of degree .
Cite
@article{arxiv.2106.08560,
title = {Quadratic points on intersections of two quadrics},
author = {Brendan Creutz and Bianca Viray},
journal= {arXiv preprint arXiv:2106.08560},
year = {2023}
}
Comments
39 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