Witt groups of Severi-Brauer varieties and of function fields of conics

2023/04/07 by Anne Quéguiner-Mathieu, Jean-Pierre Tignol · 1 voice
Mathematics · #math.KT

paper · pdf · doi:10.46298/epiga.2024.11171

Abstract

The Witt group of skew hermitian forms over a division algebra D with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of D with values in a suitable line bundle. In the special case where D is a quaternion algebra we extend previous work by Pfister and by Parimala on the Witt group of conics to set up two five-terms exact sequences relating the Witt groups of hermitian or skew-hermitian forms over D with the Witt groups of the center, of the function field of the Severi-Brauer conic of D, and of the residue fields at each closed point of the conic.

Discussions

• Anne Qu\'eguiner-Mathieu, Jean-Pierre Tignol Witt groups of Severi-Brauer varieties and of function fields of conics https://arxiv.org/abs/2304.03539 [bsky, 0 points, 0 comments]

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