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# Homology, Homotopy and Applications

## Volume 12 (2010)

### Number 1

### La cohomologie totale est un foncteur dérivé

Pages: 367 – 400

DOI: http://dx.doi.org/10.4310/HHA.2010.v12.n1.a19

#### Author

#### Abstract

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.

#### Keywords

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

#### 2010 Mathematics Subject Classification

17B66, 32M05, 32M25