
TL;DR
This paper proves a fundamental lemma related to constructible sheaves, providing a motivic proof of a classical theorem, and clarifies the categorical structure and properties of constructible sheaves in algebraic geometry.
Contribution
It establishes the basic lemma's proof, connects constructible sheaves with the derived category, and demonstrates key properties like effaceability within the category.
Findings
Proof of the basic lemma by Beilinson
Equivalence of categories for constructible sheaves
Effaceability of higher direct images and Ext groups
Abstract
This article contains a proof of the basic lemma. This lemma, discovered by Beilinson, yields a motivic proof of the Andreotti-Frankel theorem for affine varieties. Next, it is shown that the 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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Geometric and Algebraic Topology
