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Local Fields

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Author(s): H. C. Johansson, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part III Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; algebra; abstract algebra; modern algebra; field theory

Introduction
Basic theory
Fields
Rings
Topological rings
The p-adic numbers
Valued fields
Hensel's lemma
Extension of norms
Newton polygons
Discretely valued fields
Teichmüller lifts
Witt vectors*
Some p-adic analysis
Ramification theory for local fields
Ramification index and inertia degree
Unramified extensions
Totally ramified extensions
Further ramification theory
Some filtrations
Multiple extensions
Local class field theory
Infinite Galois theory
Unramified extensions and Weil group
Main theorems of local class field theory
Lubin–Tate theory
Motivating example
Formal groups
Lubin–Tate extensions
Index