Seminar Algebra and Geometry: Andreas Maurischat (Universität Heidelberg)

Galois groups for inseparable field extensions

In Hopf-Galois theory one can attach a Hopf algebra H (resp.  an affine group scheme G=Spec(H) ) to any finite field extension. In general, however, this Hopf-algebra is not unique, but in some cases - e.g. normal separable extensions - there are natural choices. In this talk, we will show how one can obtain "natural choices" for finite extensions (even inseparable ones) by imposing an extra structure on the field, namely a so-called iterative derivation.

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