A motivic construction of the de Rham-Witt complex
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910282765303808 |
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| author | Koizumi, Junnosuke Miyazaki, Hiroyasu |
| author_facet | Koizumi, Junnosuke Miyazaki, Hiroyasu |
| contents | The theory of reciprocity sheaves due to Kahn-Saito-Yamazaki is a powerful framework to study invariants of smooth varieties via invariants of pairs $(X,D)$ of a variety $X$ and a divisor $D$. We develop a generalization of this theory where $D$ can be a $\mathbb{Q}$-divisor. As an application, we provide a motivic construction of the de Rham-Witt complex, which is analogous to the motivic construction of the Milnor $K$-theory due to Suslin-Voevodsky. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05846 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A motivic construction of the de Rham-Witt complex Koizumi, Junnosuke Miyazaki, Hiroyasu Algebraic Geometry Number Theory 14F42 (13F35, 14F30, 19E15) The theory of reciprocity sheaves due to Kahn-Saito-Yamazaki is a powerful framework to study invariants of smooth varieties via invariants of pairs $(X,D)$ of a variety $X$ and a divisor $D$. We develop a generalization of this theory where $D$ can be a $\mathbb{Q}$-divisor. As an application, we provide a motivic construction of the de Rham-Witt complex, which is analogous to the motivic construction of the Milnor $K$-theory due to Suslin-Voevodsky. |
| title | A motivic construction of the de Rham-Witt complex |
| topic | Algebraic Geometry Number Theory 14F42 (13F35, 14F30, 19E15) |
| url | https://arxiv.org/abs/2301.05846 |