Higher $K$-theory of forms III: from chain complexes to derived categories
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915020012519424 |
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| author | Marlowe, Daniel Schlichting, Marco |
| author_facet | Marlowe, Daniel Schlichting, Marco |
| contents | We exhibit a canonical equivalence between the hermitian $K$-theory (alias Grothendieck-Witt) spectrum of an exact form category and that of its derived Poincaré $\infty$-category, with no assumptions on the invertibility of $2$. Along the way, we obtain a model for the nonabelian derived functor of a nondegenerate quadratic functor on an exact category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher $K$-theory of forms III: from chain complexes to derived categories Marlowe, Daniel Schlichting, Marco K-Theory and Homology We exhibit a canonical equivalence between the hermitian $K$-theory (alias Grothendieck-Witt) spectrum of an exact form category and that of its derived Poincaré $\infty$-category, with no assumptions on the invertibility of $2$. Along the way, we obtain a model for the nonabelian derived functor of a nondegenerate quadratic functor on an exact category. |
| title | Higher $K$-theory of forms III: from chain complexes to derived categories |
| topic | K-Theory and Homology |
| url | https://arxiv.org/abs/2411.09401 |