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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.

##### MSC:
 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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