"Scheme-theoretic images" of morphisms of stacks

TL;DR

This paper establishes criteria for the existence of scheme-theoretic images of morphisms from algebraic stacks to other stacks and applies these to demonstrate algebraicity of certain moduli stacks of local Galois representations.

Contribution

It introduces new criteria for scheme-theoretic images of morphisms of stacks and applies them to prove algebraicity of specific moduli stacks.

Findings

Criteria for scheme-theoretic images of morphisms of stacks.

Certain moduli stacks of local Galois representations are algebraic or Ind-algebraic.

Application of criteria to algebraicity problems in stack theory.

Abstract

We give criteria for certain morphisms from an algebraic stack to a (not necessarily algebraic) stack to admit an (appropriately defined) scheme-theoretic image. We apply our criteria to show that certain natural moduli stacks of local Galois representations are algebraic (or Ind-algebraic) stacks.