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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2508.05184 |
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| _version_ | 1866912526903541760 |
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| author | Banerjee, Sourayan |
| author_facet | Banerjee, Sourayan |
| contents | Homotopy invariance of $K$-theory has always been a point of interest. In this article, with the help of the generators of Nil$K$-groups using Grayson's technique, it is shown that if $R$ is a Prüfer domain, then $K_n(R) \cong K_n(R[s])$ for all $n>0.$ This is a specific case of the already published work of the author and Vivek Sadhu. However, contrary to the method used before, we specifically prove the isomorphism by showing that Nil$K$-groups vanish. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homotopy Invariance of $K$-groups using Grayson's Technique Banerjee, Sourayan K-Theory and Homology 19D06 (Primary) 19D35, 18E10 Secondary Homotopy invariance of $K$-theory has always been a point of interest. In this article, with the help of the generators of Nil$K$-groups using Grayson's technique, it is shown that if $R$ is a Prüfer domain, then $K_n(R) \cong K_n(R[s])$ for all $n>0.$ This is a specific case of the already published work of the author and Vivek Sadhu. However, contrary to the method used before, we specifically prove the isomorphism by showing that Nil$K$-groups vanish. |
| title | Homotopy Invariance of $K$-groups using Grayson's Technique |
| topic | K-Theory and Homology 19D06 (Primary) 19D35, 18E10 Secondary |
| url | https://arxiv.org/abs/2508.05184 |