Chow Groups: A Structure Theorem, RIEMANN-ROCH without denominators and ARTIN approximation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911918054178816 |
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| author | Dutta, S. P. |
| author_facet | Dutta, S. P. |
| contents | The focus of this note is on the Chow group problem over ramified regular local rings $(R, m)$. Our goal is threefold: i) to introduce a characterization of a ramified regular local ring essentially of finite type over a dvr, ii) to address the question whether $(i-1)!$ $\mathbb{A}^i(U)=0$ for specific open subsets $U$ of Spec$R$ and iii) to establish a constructive relation between Chow groups of the henselization $(R^h, m^h)$ and Chow groups of the completion $(\hat{R}, \hat{m})$ of $(R, m)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chow Groups: A Structure Theorem, RIEMANN-ROCH without denominators and ARTIN approximation Dutta, S. P. Commutative Algebra Algebraic Geometry Primary: 13D22, 14C40, Secondary: 13H05 The focus of this note is on the Chow group problem over ramified regular local rings $(R, m)$. Our goal is threefold: i) to introduce a characterization of a ramified regular local ring essentially of finite type over a dvr, ii) to address the question whether $(i-1)!$ $\mathbb{A}^i(U)=0$ for specific open subsets $U$ of Spec$R$ and iii) to establish a constructive relation between Chow groups of the henselization $(R^h, m^h)$ and Chow groups of the completion $(\hat{R}, \hat{m})$ of $(R, m)$. |
| title | Chow Groups: A Structure Theorem, RIEMANN-ROCH without denominators and ARTIN approximation |
| topic | Commutative Algebra Algebraic Geometry Primary: 13D22, 14C40, Secondary: 13H05 |
| url | https://arxiv.org/abs/2406.09724 |