Anne Quéguiner-Mathieu ; Jean-Pierre Tignol - Witt groups of Severi-Brauer varieties and of function fields of conics

epiga:11171 - Épijournal de Géométrie Algébrique, February 28, 2025, Volume 9 - https://doi.org/10.46298/epiga.2024.11171
Witt groups of Severi-Brauer varieties and of function fields of conicsArticle

Authors: Anne Quéguiner-Mathieu ; Jean-Pierre Tignol

    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.


    Volume: Volume 9
    Published on: February 28, 2025
    Accepted on: August 7, 2024
    Submitted on: April 10, 2023
    Keywords: Mathematics - K-Theory and Homology,19G12, 11E81, 14H05

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