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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.02413 |
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Table of 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.