Weil Restriction and the Quot scheme

TL;DR

This paper introduces a generalized concept called module restriction, extends Weil restriction, and proves the representability of Grothendieck's Quot functor for certain algebraic spaces.

Contribution

It generalizes Weil restriction through module restriction and demonstrates the representability of the Quot functor for separated algebraic spaces.

Findings

Module restriction generalizes Weil restriction.

Proved existence and étaleness of module restriction.

Grothendiecks Quot functor is representable for certain algebraic spaces.

Abstract

We introduce a concept that we call module restriction, which generalizes the classical Weil restriction. We first establish some fundamental properties, as existence and \'etaleness. Then we apply our results to show that Grothendiecks Quot functor parameterizing finite and flat quotients of a given quasi-coherent sheaf on a separated algebraic space, is representable.