Eric Ahlqvist: Operations on étale sheaves of sets

Rydh showed in 2011 that any unramified morphism f of algebraic spaces (algebraic stacks) has a canonical and universal factorization through an algebraic space (algebraic stack) called the étale envelope of f, where the first morphism is a closed immersion and the second is étale. We show that when f is étale then the étale envelope can be described by applying the left adjoint of the pullback of f to the constant sheaf defined by a pointed set with two elements. When f is a monomorphism locally of finite type we have a similar construction using the direct image with proper support.

Supervisor: David Rydh