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43-page Monograph in Preprint form, free download of PDF , in French.

Abstract:

This is a valuable presentation of Cohomology Descent theory including further developments of A. Grothendieck's Descent Theory. The following topics are derived from the preprint's contents: topology of descent, sheaf cohomology, category of S-schemes, D-simplicial space defined by functors, simplicial scheme, e'tale simplicial topos, category of functorial morphisms, ... References Cited: [1] The'orie des topos et cohomologie 'etale des sche'mas. Tome 2. Springer-Verlag, Berlin, 1972. Se'minaire de Ge'ome'trie Alge'brique du Bois-Marie 1963--1964 (SGA 4), Dirige' par M. Artin, A. Grothendieck et J. L. Verdier. (Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat, Lecture Notes in Mathematics, Vol. 270.); (Theory of Topoi and 'Etale Cohomology of Schemes, vol. 2, or SGA-2, directed by M. Artin, A. Grothendieck et J. L. Verdier, in collab. with N. Bourbaki, P. Deligne et B. Saint-Donat). [2] Pierre Deligne. The'orie de Hodge. III. Inst. Hautes E'tudes Sci. (IHES), Publ. Math., (44) :5--77, 1974. [3] Jean Giraud. Cohomologie non abe'lienne. ("Non--Abelian Cohomology.") Springer-Verlag, Berlin, 1971. Die Grundlehren der mathematischen Wissenschaften, Band 179. [4] A. Grothendieck. R^evetements e'tales et groupe fondamental. Springer--Verlag, Berlin, Heidelberg, New York, 1971. Lectures Notes in Math., 224. Free downloads at: http://www.math.polytechnique.fr/~laszlo/adique/descente.pdf

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open access: http://www.math.polytechnique.fr/~laszlo/adique/descente.pdf

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Adescente_Laszlo.pdf

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