The four functors of Grothendieck in examples

Tuesday, May 01st, 2012 | Author:

This post will discuss the definition of the four functors "pushforward" f_\ast, "pullback" f^\ast, "pushforward with compact support" f_{!} and "exceptional pullback" f^{!} of sheaves of abelian groups, associated to a continuous morphism f : X \to Y of topological spaces X and Y. Then we will look at maps f which are open immersions or closed immersions, and calculate in the example of \mathbb{C}^\times \to \mathbb{C} and its closed complement \{0\} \to \mathbb{C} exactly what happens. This is intended to give some intuition what the general four functor calculus is about.

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Category: English, Mathematics | 2 Comments