Weil Restriction and the Quot scheme

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 étaleness. 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.

In the previous version the section about étaleness was wrong. Moreover, several statements about non-commutative rings were imprecise, unclear if not false. In this version we have rewritten the section concerning étaleness, and we have corrected statements concerning non-commutative rings