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2019 Differential characters of Drinfeld modules and de Rham cohomology
James Borger, Arnab Saha
Algebra Number Theory 13(4): 797-837 (2019). DOI: 10.2140/ant.2019.13.797

Abstract

We introduce differential characters of Drinfeld modules. These are function-field analogues of Buium’s p-adic differential characters of elliptic curves and of Manin’s differential characters of elliptic curves in differential algebra, both of which have had notable Diophantine applications. We determine the structure of the group of differential characters. This shows the existence of a family of interesting differential modular functions on the moduli of Drinfeld modules. It also leads to a canonical F-crystal equipped with a map to the de Rham cohomology of the Drinfeld module. This F-crystal is of a differential-algebraic nature and the relation to the classical cohomological realizations is presently not clear.

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James Borger. Arnab Saha. "Differential characters of Drinfeld modules and de Rham cohomology." Algebra Number Theory 13 (4) 797 - 837, 2019. https://doi.org/10.2140/ant.2019.13.797

Information

Received: 3 September 2017; Revised: 26 November 2018; Accepted: 22 February 2019; Published: 2019
First available in Project Euclid: 18 May 2019

zbMATH: 07059757
MathSciNet: MR3951581
Digital Object Identifier: 10.2140/ant.2019.13.797

Subjects:
Primary: 11G99
Secondary: 14L05

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 4 • 2019
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