#### Vol. 13, No. 4, 2019

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editors' Interests Submission Guidelines Submission Form Editorial Login Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Differential characters of Drinfeld modules and de Rham cohomology

### James Borger and Arnab Saha

Vol. 13 (2019), No. 4, 797–837
##### 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.

##### Keywords
arithmetic geometry, number theory, algebraic geometry, arithmetic jet spaces, Witt vectors, Drinfeld modules, differential characters, de Rham cohomology
Primary: 11G99
Secondary: 14L05