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Perverse coherent sheaves. (English) Zbl 1205.18010
The authors introduce the analogue of perverse \(t\)-structure on the derived category of an algebraic stack satisfying some mild technical conditions.
In the first section some basic properties of (quasi-)coherent sheaves on stacks are established. In particular, the existence of a dualizing complex is studied. The authors then go on to define two subcategories depending on a perversity function. If the perversity function is monotone and comonotone, then these categories define a \(t\)-structure on the (un-)bounded derived category of coherent sheaves on a Noetherian scheme or, more generally, a Noetherian semi-separated stack \(X\) admitting a dualizing complex.
Under certain additional assumptions more can be said. In particular, one can then prove that the category of perverse coherent sheaves is Artinian and Noetherian.

18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
14A20 Generalizations (algebraic spaces, stacks)
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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