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Galois theory: Characteristic p vs. characteristic 0

4:00 pm Thursday, October 3, 2013
Andrew Obus (Virginia)

We often try to understand fields by studying their finite Galois extensions. The characteristic of the field plays a large role in how these extensions look---in particular, extracting pth roots of elements in a field of characteristic p never gives a Galois extension! However, it is often possible to "bridge the gap" between characteristic p and characteristic 0. We will discuss this in two cases:

1) The striking result of Fontaine-Wintenberger on the isomorphism of the absolute Galois groups of two particular complete fields, one in characteristic p and one in characteristic 0.

2) The Oort Conjecture (now a theorem of the speaker, Stefan Wewers, and Florian Pop) and the local lifting problem, comparing Galois extensions arising from branched covers of curves in characteristic p and in characteristic 0.

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