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위키데이터

• ID : Q1095535

말뭉치

1. In this text, we generalize Čech cohomology to sheaves F with values in blue B-modules where B is a blueprint with −1.
2. One problem with Čech cohomology is that a short exact sequence of sheaves doesn’t induce a long exact sequence of sheaves.
3. I could now compute the Čech cohomology of a lot of stuff explicitly, for instance sheaves on projective space.
4. In this section, we are going to show that Čech cohomology and sheaf cohomology of quasi-coherent sheaves agree in nice cases.
5. We generalize Čech cohomology theory and invertible sheaves to semiring schemes.
6. Often one speaks also of Čech cohomology instead of Aleksandrov–Čech cohomology.
7. In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space.
8. For such a cover, the Čech cohomology of X is defined to be the simplicial cohomology of the nerve.
9. The Čech cohomology of X is defined by considering refinements of open covers.
10. For less well-behaved spaces, Čech cohomology differs from singular cohomology.
11. In this text, we generalize Cech cohomology to sheaves  with values in blue B-modules where B is a blueprint with −1.
12. Therefore if F is a quasi-coherent sheaf on a variety, the sheaf cohomology of F can be computed using Cech cohomology with respect to a Zariski open cover.
13. Hence Čech cohomology is more an algorithm for computing cohomology (see also at Čech methods) than a cohomology theory in itself.
14. If these conditions do not apply, then the definition of Cech cohomology groups still works as such, but typically no longer qualifies as a “cohomology theory”, axiomatically.
15. Often Cech cohomology is considered for the case that A • A_\bullet is concentrated in a single degree, in which case the first term in the sum defining the differential in def.

메타데이터

위키데이터

• ID : Q1095535

Spacy 패턴 목록

• [{'LOWER': 'čech'}, {'LEMMA': 'cohomology'}]