Kummer-Artin-Schreier-Witt theory and Cartier theory
Abstract. It was shown that there exist exact sequences of group
schemes over a ring of mixed characteristics, which unify the Kummer
sequences and the Artin-Schreier-Witt sequences, in a jount work
of Sekiguchi and Suwa.
In this talk, the Kummer-Artin-Shreier-Witt theory can be described
in the framework of the Cartier theory on commutative formal groups.
We can translate the problem to construct group schemes appearing
in the Kummer-Artin-Schreier-Witt theory to a problem of linear algebra
on the Dieudonne-Cartier algebras, with help of formal power series
generalizing the Artin-Hasse exponential series.