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arXiv · 2604.00581

Cohomological invariants of hermitian forms that detect hyperbolicity

Yong Hu·Alexandre Lourdeaux
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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.

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BibTeXRIS

Yong Hu, Alexandre Lourdeaux. 2026-04-01. Cohomological invariants of hermitian forms that detect hyperbolicity. https://arxiv.org/abs/2604.00581

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