English

Symmetric versus genuine symmetric forms in Hermitian K-theory

K-Theory and Homology 2025-06-23 v3

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.

Keywords

Cite

@article{arxiv.2503.14288,
  title  = {Symmetric versus genuine symmetric forms in Hermitian K-theory},
  author = {Marco Schlichting},
  journal= {arXiv preprint arXiv:2503.14288},
  year   = {2025}
}

Comments

Improved bounds in mixed characteristic, proof of Flat Excision rewritten