Chow-Witt rings of split quadrics
K-Theory and Homology
2019-09-02 v2 Algebraic Geometry
Algebraic Topology
Abstract
We compute the Chow-Witt rings of split quadrics over a field of characteristic not two. We even determine the full bigraded I-cohomology and Milnor-Witt cohomology rings, including twists by line bundles. The results on I-cohomology corroborate the general philosophy that I-cohomology is an algebro-geometric version of singular cohomology of real varieties: our explicit calculations confirm that the I-cohomology ring of a split quadric over the reals is isomorphic to the singular cohomology ring of the space of its real points.
Keywords
Cite
@article{arxiv.1811.12685,
title = {Chow-Witt rings of split quadrics},
author = {Jens Hornbostel and Heng Xie and Marcus Zibrowius},
journal= {arXiv preprint arXiv:1811.12685},
year = {2019}
}
Comments
This is the final version. Some additional details have been added, and a sign ambiguity of the previous version has been resolved