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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.31 no.2 Antofagasta June 2012 

Proyecciones Journal of Mathematics Vol. 31, No 2, pp. 165-168, June 2012. Universidad Católica del Norte Antofagasta - Chile


Hochschild-Serre Statement for the total cohomology


François Lescure

Universite de Lille 1, France


Let M be a complex manifold and F a Om-module with a g-holomorphic action where g is a complex Lie algebra (cf. [3]). We denote by H(g, F) the "total cohomology" as defined in [1] [2]. Then we prove that, for any ideal a c g,the module H* (a, F) viewed as a g/a-module, we have a spectral sequence which converges to H(g, F).


[1] F. Lescure, Action sur la cohomologie de Dolbeault, C. R. Acad. Sci., 314, pp. 923-926, (1992).

[2] F. Lescure, Cohomologie totale et courants de Dolbeault invariants, J. reine angew. Math., 475, pp. 103-136, (1996).

[3] F. Lescure La cohomologie totale est un foncteur derive, Homology, Homotopy and Applications, Volume 12, Number 1, pp. 367-400, (2010).

Received : February 2012. Accepted : March 2012

Francois Lescure

U.M.R. CNRS 8524

U.F.R. de Mathóematiques

Universitóe de Lille 1

59655 Villeneuve d'Ascq Cedex


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