×

zbMATH — the first resource for mathematics

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)
PDF BibTeX XML Cite
Full Text: Link arXiv