Hopf-Galois Extensions and Applications

Hopf-Galois Extensions and Applications
Abstract: Hopf-Galois theory is a generalization of the classical Galois theory. The concept of Hopf-Galois extension is due to Chase and Sweedler. They introduced it in 1969 to study purely inseparable extensions of fields and ramified extensions of rings. Then, in 1987, Greither and Pareigis developed Hopf-Galois theory for separable field extensions.
In this talk, we first describe minimal Hopf-Galois structures of separable field extensions. Then we present normal bases of some Hopf-Galois extensions, namely those constructed from algebraic curves. And then we describe the resulting arithmetic properties.
Speaker(s)Tony Ezome (École Normale Supérieure - ENS, Libreville, Gabon and Pole of Research in Mathematics and Applications in Africa - PREMA)