Title: Differential Characters of Drinfeld Modules and de Rham Cohomology,
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.