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Hodge Theory and Complex Algebraic Geometry I by Claire Voisin, Leila Schneps

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4

Sheaves and Cohomology

In this chapter, we introduce several very general objects, which will be used to interpret the results of Hodge theory concerning the de Rham cohomology of a Kähler manifold, and to apply them from a more theoretical and conceptual point of view. First, we need to introduce the notion of a sheaf (of abelian groups, rings, modules, etc.) over a topological space X. A sheaf is the following collection of data: a group (ring, module, etc.) of sections of F on U, for each open set U of X, together with restriction maps ...

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