Orbital integrals on unitary groups over local fields in positive characteristic converge absolutely.
Scharlau, Quadratic and Hermitian Forms, Grundlehren math.\ Wiss., vol
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The Witt group of skew hermitian forms over a division algebra D with symplectic involution is canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of D with values in a suitable line bundle; for quaternion algebras, two five-term exact sequences relate
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Convergence of orbital integrals on unitary groups in positive characteristic
Orbital integrals on unitary groups over local fields in positive characteristic converge absolutely.
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Witt groups of Severi-Brauer varieties and of function fields of conics
The Witt group of skew hermitian forms over a division algebra D with symplectic involution is canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of D with values in a suitable line bundle; for quaternion algebras, two five-term exact sequences relate