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arXiv · 1811.12685

Chow-Witt rings of split quadrics

Jens Hornbostel·Heng Xie·Marcus Zibrowius
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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.

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Jens Hornbostel, Heng Xie, Marcus Zibrowius. 2018-11-30. Chow-Witt rings of split quadrics. https://arxiv.org/abs/1811.12685

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