Perverse \(t\)-structure on Artin stacks
The article under review gives an account of the basic theory of perverse sheaves, with finite or adic coefficients, on an Artin stack \(\mathcal X\) locally of finite type over a field \(k\). Its main contribution is to define the category of perverse sheaves on \(\mathcal X\) in a way that mimics the usual definition for schemes, namely as the heart of a \(t\)-structure on an appropriate derived category of constructible sheaves on \(\mathcal X\); and to show that this is essentially the only possible definition compatible with the usual definition of perverse sheaves on a scheme and with descent. The article also contains basic material on middle extensions; Artinianness and Noetherianness of the category of perverse sheaves with \(\mathbb Q_l\)-coefficients for \(l \in k^\times\), and a characterization of the simple perverse sheaves in this case; and the theory of weights when \(k\) is finite.
scientific article; zbMATH DE number 5533149