Change of Coefficients for Drinfeld Modules, Shtuka, and Abelian Sheaves

TL;DR

This paper investigates how changing the coefficient rings in Drinfeld modules, shtuka, and abelian sheaves affects their moduli spaces, revealing proper but non-representable morphisms.

Contribution

It introduces a new morphism between moduli spaces induced by coefficient change, extending to shtuka and abelian sheaves, with detailed properties.

Findings

The morphism from A'-modules to A-modules is proper.

This morphism is generally not representable.

Results extend to shtuka and abelian sheaves.

Abstract

We study the passage from Drinfeld-A'-modules to Drinfeld-A-modules for a given finite flat inclusion A \subset A'. We show that this defines a morphism from the moduli space of Drinfeld-A'-modules to the moduli space of Drinfeld-A-modules which is proper but in general not representable. For Drinfeld-Anderson shtuka and abelian sheaves instead of Drinfeld modules we obtain the same results.