Drinfeld Modules and Lifts of Frobenius in Positive Characteristic

Abstract: 

We develop the theory of δδ-characters for Drinfeld modules that is analogous to differential characters for abelian varieties due to Fuchs and Manin. We replace the notion of derivation for function fields with ππ-derivation or equivalently lift of Frobenius and show the existence of δδ-characters for Drinfeld modules. If time permits, we will also talk about differential modular forms which is a larger class containing the usual modular forms and contains interesting elements that have no classical analogue.