Galois characteristics of local fields

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• Marius Leonhardt, University of Cambridge
• Friday 11 November 2016, 15:00-16:00
• CMS, MR15.

If you have a question about this talk, please contact Nicolas Dupré.

What characteristics of a field can be deduced from its absolute Galois group? Does the Galois group uniquely determine the field? It turns out that the answer to this question depends on the “type” of field. For example, any two finite fields have isomorphic absolute Galois groups, whereas two number fields are isomorphic if and only if their Galois groups are. In the case of finite extensions of $\Q_p$, there are non-isomorphic fields with isomorphic Galois groups. However, if one requires the group isomorphism to respect the filtration given by the ramification subgroups, then S. Mochizuki has showed that one can fully reconstruct the field. In this talk I will give an overview of the methods involved in Mochizuki’s proof, focussing on local class field theory on the one hand and Hodge-Tate representations on the other.

This talk is part of the Junior Algebra and Number Theory seminar series.

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