Blown-up Čech cohomology and Cartan's Theorem B on real algebraic varieties
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866913225247817728 |
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| author | Kowalczyk, Tomasz |
| author_facet | Kowalczyk, Tomasz |
| contents | We introduce a concept of blown-up Čech cohomology for coherent sheaves of homological dimension $\leq 1$ and some quasi-coherent sheaves on a non-singular real affine variety. Its construction involves a directed set of multi-blowups. We establish, in particular, long exact cohomology sequence and Cartan's Theorem B. Finally, some applications are provided, including universal solution to the first Cousin problem (after blowing up). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_10034 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Blown-up Čech cohomology and Cartan's Theorem B on real algebraic varieties Kowalczyk, Tomasz Algebraic Geometry 14P05, 14F05, 13D05 We introduce a concept of blown-up Čech cohomology for coherent sheaves of homological dimension $\leq 1$ and some quasi-coherent sheaves on a non-singular real affine variety. Its construction involves a directed set of multi-blowups. We establish, in particular, long exact cohomology sequence and Cartan's Theorem B. Finally, some applications are provided, including universal solution to the first Cousin problem (after blowing up). |
| title | Blown-up Čech cohomology and Cartan's Theorem B on real algebraic varieties |
| topic | Algebraic Geometry 14P05, 14F05, 13D05 |
| url | https://arxiv.org/abs/1809.10034 |