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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.14288 |
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| _version_ | 1866908414367498240 |
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| author | Schlichting, Marco |
| author_facet | Schlichting, Marco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetric versus genuine symmetric forms in Hermitian K-theory Schlichting, Marco K-Theory and Homology 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. |
| title | Symmetric versus genuine symmetric forms in Hermitian K-theory |
| topic | K-Theory and Homology |
| url | https://arxiv.org/abs/2503.14288 |