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arXiv · 2503.14288

Symmetric versus genuine symmetric forms in Hermitian K-theory

Marco Schlichting
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Abstract

We show that for finite dimensional regular Noetherian rings that contain a field or are smooth over a Dedekind domain, the comparison map from the Hermitian K-theory of genuine symmetric forms to that of symmetric forms is an equivalence in degrees greater or equal -1 and a monomorphism in degree -2. In particular, the spaces of Hermitian K-theory of genuine symmetric forms and the symplectic K-theory space are homotopy invariant for such rings.

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Marco Schlichting. 2025-03-18. Symmetric versus genuine symmetric forms in Hermitian K-theory. https://arxiv.org/abs/2503.14288

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