Homology, Homotopy and Applications

La cohomologie totale est un foncteur dérivé

François Lescure

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We use a certain sheaf of associative rings to define a global Ext functor. We prove that the "cohomologie totale" which we defined in an earlier paper in an analytic way is given by this global Ext. We use this functorial definition to prove some results conjectured in earlier papers. We introduce the "anchor spectral sequence" and use it to give a precise description of the total cohomology for the special case of complex homogeneous spaces.

Article information

Homology Homotopy Appl., Volume 12, Number 1 (2010), 367-400.

First available in Project Euclid: 28 January 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10] 32M25: Complex vector fields 17B66: Lie algebras of vector fields and related (super) algebras

Lie algebra of vector fields complex vector fields complex Lie groups groups of automorphisms acting on complex spaces


Lescure, François. La cohomologie totale est un foncteur dérivé. Homology Homotopy Appl. 12 (2010), no. 1, 367--400. https://projecteuclid.org/euclid.hha/1296223835

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