Constructible sheaves

Abstract

This article contains a proof of the basic lemma, which yields a motivic proof of the Andreotti Frankel theorem for affine varieties. Next, it is shown that the triangulated category of "Cohomologically Constructible Sheaves" (as it is referred to in the Riemann-Hilbert correspondence) coincides with the derived category of bounded complexes of constructible sheaves. It is also shown that higher direct images and the sheaf-Ext groups are effaceable in the category of constructible sheaves.