Algebraic $K$-theory of coherent spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909846696099840 |
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| author | Lehner, Georg |
| author_facet | Lehner, Georg |
| contents | We give a description of the value of a finitary localizing invariant, such as algebraic $K$-theory, on the category of sheaves on a locally coherent space $X$. This in particular includes all spaces that arise as spectra of commutative rings. As applications we discuss the connection between scissors congruence $K$-theory and Topological Hochschild Homology of certain locally coherent spaces, as well as the algebraic $K$-theory of a measure space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic $K$-theory of coherent spaces Lehner, Georg K-Theory and Homology Category Theory General Topology Primary: 19D99, Secondary: 06D22, 54B40, 18F20 We give a description of the value of a finitary localizing invariant, such as algebraic $K$-theory, on the category of sheaves on a locally coherent space $X$. This in particular includes all spaces that arise as spectra of commutative rings. As applications we discuss the connection between scissors congruence $K$-theory and Topological Hochschild Homology of certain locally coherent spaces, as well as the algebraic $K$-theory of a measure space. |
| title | Algebraic $K$-theory of coherent spaces |
| topic | K-Theory and Homology Category Theory General Topology Primary: 19D99, Secondary: 06D22, 54B40, 18F20 |
| url | https://arxiv.org/abs/2507.00221 |