2025/04/11 by Nicolas Garrel, Garrel, Nicolas
Mathematics · #11E81 #12G05 #16W70 #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2504.08920
openalex publication_date 2025/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe all Witt invariants of anti-hermitian forms over a quaternion algebra with its canonical involution, and in particular all Witt invariants of orthogonal groups O(A,σ) where (A,σ) is an central simple algebra with orthogonal involution and A has index 2. They are combinations of appropriately defined λ-powers, similarly to the case of quadratic forms, but the module of invariants is no longer free over those operations. The method involves extending the scalars to a generic splitting field of A, and controlling the residues of the invariants with respect to valuations coming from closed points in the Severi-Brauer variety.