Starts 16 Jun 2023 14:00
Ends 16 Jun 2023 15:00
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Hopf-Galois Extensions and Applications
HYBRID
Leonardo da Vinci Bldg - Luigi Stasi Seminar Room and Zoom
This is a hybrid event.
To attend in remote, kindly register in advance through https://zoom.us/meeting/register/tJcvcOyvqjsjHd39bPbAAAYWQIWsCbRU208s
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.