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.

Category: English, Mathematics | 2 Comments