1. La suite exacte de Mayer–Vietoris en cohomologie de Čech.
- Author
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TÃate, Claire
- Subjects
- *
MATHEMATICAL sequences , *COHOMOLOGY theory , *MATHEMATICAL complexes , *COMMUTATIVE rings , *KOSZUL algebras - Abstract
Abstract: This article is about the foundation of the Mayer–Vietoris exact sequence in Čech cohomology, with respect to the augmented Čech complex, often called “the stable Koszul complex”. Our treatment is elementary and uses neither the local cohomology of Grothendieck nor the widespread noetherian local cohomology. We use explicit objects giving us an elementary algebraic treatment in a general nonnoetherian context, i.e. two finite sequences , of a commutative ring and some Čech complexes built from these sequences. More precisely, our strategy consists in producing a short exact sequence of “type Čech“ complexes having the expected cohomologies. Then arises a simplicial complex on the set with a relatively surprising combinatory. [Copyright &y& Elsevier]
- Published
- 2014
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