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arXiv · 1809.10034

Blown-up \v{C}ech cohomology and Cartan's Theorem B on real algebraic varieties

Tomasz Kowalczyk
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Abstract

We introduce a concept of blown-up \v{C}ech 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).

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Tomasz Kowalczyk. 2018-09-26. Blown-up \v{C}ech cohomology and Cartan's Theorem B on real algebraic varieties. https://doi.org/10.1142/s0129167x19500423

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