Cohomological invariants of hermitian forms that detect hyperbolicity

Summary · qwen2.5:32b

Researchers constructed cohomological invariants for hermitian forms using unramified cohomology groups that detect hyperbolicity, applicable across any type (orthogonal, symplectic, unitary) and over fields with any characteristic; this method shows that hermitian pairs over quaternion algebras with trivial classical invariants are hyperbolic in fields of separable dimension 3.

Excerpt

arXiv:2604.00581v2 Announce Type: replace Abstract: By using unramified cohomology groups, we construct a full sequence of cohomological invariants for hermitian forms of any (orthogonal, symplectic or unitary) type that can be used to detect hyperbolicity. The base central simple algebra can have arbitrary degree and the base field can have arbitrary characteristic. In the orthogonal case, we work with hermitian pairs, and we apply our construction to show that over fields of separable dimension 3, hermitian pairs over quaternion algebras with trivial classical invariants are hyperbolic. This last result extends a result of Berhuy to arbitrary characteristic.