Mathematics

Dr. Arnab Saha
Australian National University

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 new canonical F-crystal that admits a filtration equipped with a map to the de Rham cohomology of the Drinfeld module, preserving the Hodge structure. This new F-crystal is of a differential-algebraic nature, and the relation to the classical cohomological realizations and p-adic Hodge theory is presently not clear.