The de Rham isomorphism for Drinfeld modules over Tate algebras

TL;DR

This paper establishes the de Rham isomorphism for Drinfeld modules over Tate algebras, linking algebraic and analytic structures, and provides criteria for their uniformizability and triviality.

Contribution

It defines the de Rham map for these modules and proves it is an isomorphism under natural conditions, advancing understanding of their structure.

Findings

De Rham map is an isomorphism under certain hypotheses

Criteria for uniformizability of Drinfeld modules over Tate algebras

Criteria for rigid analytic triviality of these modules

Abstract

Introduced by Angl\`{e}s, Pellarin, and Tavares Ribeiro, Drinfeld modules over Tate algebras are closely connected to Anderson log-algebraicity identities, Pellarin $L$-series, and Taelman class modules. In the present paper we define the de Rham map for Drinfeld modules over Tate algebras, and we prove that it is an isomorphism under natural hypotheses. As part of this investigation we determine further criteria for the uniformizability and rigid analytic triviality of Drinfeld modules over Tate algebras.