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Blown-up Čech cohomology and Cartan’s Theorem B on real algebraic varieties

Tomasz Kowalczyk

Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Profesora Łojasiewicza 6, 30-348 Kraków, Poland

E-mail Address: tomek.kowalczyk@student.uj.edu.pl

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https://doi.org/10.1142/S0129167X19500423Cited by:0 (Source: Crossref)

Abstract

We introduce a concept of blown-up Čech cohomology for coherent sheaves of homological dimension $\leq 1$ $\leq 1$ and some quasi-coherent sheaves on a nonsingular 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).

Keywords:

AMSC: 14P05, 14F05, 13D05

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