Artin perverse sheaves

Abstract

We show that the perverse t-structure induces a t-structure on the category DA(S,Zℓ) of Artin ℓ-adic complexes when S is an excellent scheme of dimension less than 2 and provide a counter-example in dimension 3. The heart PervA(S,Zℓ) of this t-structure can be described explicitly in terms of representations in the case of 1-dimensional schemes.When S is of finite type over a finite field, we also construct a perverse homotopy t-structure over DA(S,Qℓ) and show that it is the best possible approximation of the perverse t-structure. We describe the simple objects of its heart PervA(S,Qℓ)# and show that the weightless truncation functor ω0 is t-exact. We also show that the weightless intersection complex ECS=ω0ICS is a simple Artin homotopy perverse sheaf. If S is a surface, it is also a perverse sheaf but it need not be simple in the category of perverse sheaves.