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Constructible sheaves. (English) Zbl 1059.14025

Parimala, R. (ed.), Proceedings of the international colloquium on algebra, arithmetic and geometry, Mumbai, India, January 4–12, 2000. Part I and II. New Delhi: Narosa Publishing House, published for the Tata Institute of Fundamental Research, Bombay (ISBN 81-7319-476-9). Stud. Math., Tata Inst. Fundam. Res. 16, 471-491 (2002).
Summary: This article contains a proof of the basic lemma, which yields a motivic proof of the Andreotti-Frankel theorem for affine varieties [A. Andreotti and T. Frankel, Ann. Math. (2) 69, 713–717 (1959; Zbl 0115.38405)]. 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.
For the entire collection see [Zbl 1013.00021].

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
18E30 Derived categories, triangulated categories (MSC2010)
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)

Citations:

Zbl 0115.38405
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