The comparison of the 0-th Suslin homology and Chow groups of 0-cycles with modulus
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915399333838848 |
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| author | Nakamura, Teppei |
| author_facet | Nakamura, Teppei |
| contents | We show that, for a $K_0$-regular projective normal surface $X$ over a perfect field $k$ of positive characteristic and a reduced effective Cartier divisor $D\hookrightarrow X$, the Chow group of zero cycles on $X$ with modulus $D$ coincides with the 0-th Suslin homology of $X\setminus D$. Moreover, we show that this isomorphism also holds for a projective smooth scheme of any dimension with a reduced effective Cartier divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03891 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The comparison of the 0-th Suslin homology and Chow groups of 0-cycles with modulus Nakamura, Teppei Algebraic Geometry Primary 14C25, Secondary 14F42, 19E15 We show that, for a $K_0$-regular projective normal surface $X$ over a perfect field $k$ of positive characteristic and a reduced effective Cartier divisor $D\hookrightarrow X$, the Chow group of zero cycles on $X$ with modulus $D$ coincides with the 0-th Suslin homology of $X\setminus D$. Moreover, we show that this isomorphism also holds for a projective smooth scheme of any dimension with a reduced effective Cartier divisor. |
| title | The comparison of the 0-th Suslin homology and Chow groups of 0-cycles with modulus |
| topic | Algebraic Geometry Primary 14C25, Secondary 14F42, 19E15 |
| url | https://arxiv.org/abs/2412.03891 |