Regularity of semi-valuation rings and homotopy invariance of algebraic K-theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914023379828736 |
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| author | Dahlhausen, Christian |
| author_facet | Dahlhausen, Christian |
| contents | We show that the algebraic K-theory of semi-valuation rings with stably coherent regular semi-fraction ring satisfies homotopy invariance. Moreover, we show that these rings are regular if their valuation is non-trivial. Thus they yield examples of regular rings which are not homotopy invariant for algebraic K-theory. On the other hand, they are not necessarily coherent, so that they provide a class of possibly non-coherent examples for homotopy invariance of algebraic K-theory. As an application, we show that Temkin's relative Riemann-Zariski spaces also satisfy homotopy invariance for K-theory under some finiteness assumption. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_02413 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity of semi-valuation rings and homotopy invariance of algebraic K-theory Dahlhausen, Christian K-Theory and Homology 19E08, 19D35 We show that the algebraic K-theory of semi-valuation rings with stably coherent regular semi-fraction ring satisfies homotopy invariance. Moreover, we show that these rings are regular if their valuation is non-trivial. Thus they yield examples of regular rings which are not homotopy invariant for algebraic K-theory. On the other hand, they are not necessarily coherent, so that they provide a class of possibly non-coherent examples for homotopy invariance of algebraic K-theory. As an application, we show that Temkin's relative Riemann-Zariski spaces also satisfy homotopy invariance for K-theory under some finiteness assumption. |
| title | Regularity of semi-valuation rings and homotopy invariance of algebraic K-theory |
| topic | K-Theory and Homology 19E08, 19D35 |
| url | https://arxiv.org/abs/2403.02413 |