The theory of perverse sheaves historically emerged from several independent directions. One of them was the theory of intersection cohomology of Goresky-MacPherson, which originally was not defined in terms of sheaf theory but rather using explicit chain complexes. Perhaps stimulated by the Kazhdan-Lusztig conjectures it was Deligne, who gave a reformulation of the notion of intersection cohomology within the setting of sheaf theory. In this form intersection cohomology can be defined also for finitely generated schemes over a field of characteristic zero, over a finite field or over the algebraic closure of a finite field.
KeywordsGrothendieck Group Distinguished Triangle Perverse Sheave Open Embedding Perverse Sheaf
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