Witt groups of Severi-Brauer varieties and of function fields of conics
(2025) Epijournal de géométrie algébrique — Vol. 9, n° 4, p. 1-27 (2025)
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- Authors
Tignol, Jean-Pierre 
- 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 invertible sheaf. 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.
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Citations
Queguiner, A., & Tignol, J.-P. (2025). Witt groups of Severi-Brauer varieties and of function fields of conics. Epijournal de géométrie algébrique, 9(4), 1-27. https://doi.org/10.46298/epiga.2024.11171 (Original work published 2025)