Moduli Space of $\Lambda$-modules on Projective Deligne-Mumford Stacks

TL;DR

This paper constructs and proves the representability of the moduli space of $ extLambda$-modules on projective Deligne-Mumford stacks, showing it is a quasi-projective scheme.

Contribution

It introduces $ extLambda$-quot-functors on stacks and establishes the moduli space of $ extLambda$-modules as a quasi-projective scheme.

Findings

The $ extLambda$-quot-functor is representable by an algebraic space.

The moduli space of $ extLambda$-modules is a quasi-projective scheme.

The paper provides foundational tools for studying $ extLambda$-modules on stacks.

Abstract

In this paper, we define $\Lambda$-quot-functors on Deligne-Mumford stacks. We prove that the $\Lambda$-quot-functor is representable by an algebraic space. Then, we construct the moduli space of $\Lambda$-modules on a projective Deligne-Mumford stack. We prove that this moduli space is a quasi-projective scheme.