Algebra/topology seminar

Speaker: Arnab Saha (Australien National University)

Title: delta-characters of Drinfeld Modules and De Rham Cohomology

Abstract: Drinfeld modules, introduced by Drinfeld himself, can be thought of as analogues of the multiplicative group or elliptic curves. One of the important $\delta$-arithmetic object that one can attach to a Drinfeld module is the group of $\delta$-characters. The elements of this group encode important diophantine information and are analogues of Manin maps in the case of elliptic curves in differential algebra. We will classify the structure of this group of $\delta$-characters which also shows the existence of a family of interesting $\delta$-modular functions on the moduli of Drinfeld modules. This also leads to a canonical subspace inside the De Rham cohomology group of the Drinfeld module. The subspace also has a canonical operator on it induced from the lift of Frobenius coming from the $\delta$-jet space theory, which we will introduce in this talk.