M.Sc. Christoph Schrade (17.00 - 17.30)

Adams Operations on Differential Algebraic K-theory.

Abstract: In this talk I want to discuss the construction of Adams operations on Differential Algebraic K-theory of smooth complex algebraic varieties.
A class in the Differential Algebraic K-theory
Kˆ(X) of a variety X combines the information of a K-theory class of X with differential forms on X(C) that represent the image of this K-theory class under the Beilinson regulator. In particular there is a map Kˆ(X) → K(X) of the Differential Algebraic K-theory of X to the K-theory of X, which should be thought of as taking the underlying K-theory class. I want to explain how one can lift the Adams operations on algebraic K-theory K(X) along this map to define Adams operations on Differential Algebraic K-theory Kˆ(X).