The de Rham isomorphism for Drinfeld modules over Tate algebras

Abstract

Introduced by Anglès, 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.

arXiv comment33 pages

References in corpus (14)

• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• Determination of the algebraic relations among special Gamma-values in positive characteristic
• Values of certain L-series in positive characteristic
• Special L-values of Drinfeld modules
• Arithmetic of positive characteristic L-series values in Tate algebras
• A Dirichlet unit theorem for Drinfeld modules
• A rapid introduction to Drinfeld modules, $t$-modules, and $t$-motives
• Linear independence of Gamma values in positive characteristic
• A Weil-Barsotti formula for Drinfeld modules
• An effective criterion for Eulerian multizeta values in positive characteristic
• Explicit formulas for Drinfeld modules and their periods
• Algebraic independence of periods and logarithms of Drinfeld modules (with an appendix by Brian Conrad)
• A class formula for L-series in positive characteristic
• Pink's theory of Hodge structures and the Hodge conjecture over function fields

Cited by in corpus (4)

• Hyperderivatives of periods and quasi-periods for Anderson $t$-modules
• Effective rigid analytic trivializations for Drinfeld modules
• Deformation of Multiple Zeta Values and Their Logarithmic Interpretation in Positive Characteristic
• A duality result about special functions in Drinfeld modules of arbitrary rank