$K$-theory of rings of continuous functions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910322262016000 |
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| author | Aoki, Ko |
| author_facet | Aoki, Ko |
| contents | We study the algebraic $K$-theory of the ring of continuous functions on a compact Hausdorff space with values in a local division ring, e.g., a local field: We compute its negative $K$-theory and show its $K$-regularity. The complex case reproves the results of Rosenberg, Friedlander--Walker, and Cortiñas--Thom. Our consideration in the real case proves two previously unconfirmed claims made by Rosenberg in 1990. The algebraic nature of our methods enables us to deal with the nonarchimedean and noncommutative cases analogously. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05257 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $K$-theory of rings of continuous functions Aoki, Ko K-Theory and Homology Commutative Algebra Algebraic Geometry General Topology We study the algebraic $K$-theory of the ring of continuous functions on a compact Hausdorff space with values in a local division ring, e.g., a local field: We compute its negative $K$-theory and show its $K$-regularity. The complex case reproves the results of Rosenberg, Friedlander--Walker, and Cortiñas--Thom. Our consideration in the real case proves two previously unconfirmed claims made by Rosenberg in 1990. The algebraic nature of our methods enables us to deal with the nonarchimedean and noncommutative cases analogously. |
| title | $K$-theory of rings of continuous functions |
| topic | K-Theory and Homology Commutative Algebra Algebraic Geometry General Topology |
| url | https://arxiv.org/abs/2402.05257 |