Iterative differentials in positive characteristic

Abstract:  In positive characteristic, derivations often don't have the wanted properties, they have in characteristic zero. For example, the constants of C(t) with respect to the derivation d/dt are equal to C if char(C)=0, but are much larger -- namely equal to C(t^p) -- if char(C)=p>0. Here, iterative derivations give an appropriate replacement in positive characteristic. Similar to differentials as universal derivations, the notion of "iterative differentials" as universal iterative derivations will be introduced as well as "iterative connections". Furthermore I will explain some parallels to "usual" derivations/differentials/connections in characteristic zero.