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A Gentle Course in Local Class Field Theory

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This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology. The book culminates with the description of the abelian extensions of local number fields, as well as the celebrated Kronecker–Weber theory, in both the local and global cases. The material will find use across disciplines, including number theory, representation theory, algebraic geometry, and algebraic topology. Written for beginning graduate students and advanced undergraduates, this book can be used in the classroom or for independent study.

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Publisher

: Cambridge University Press., 2018

Collation

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Language

English

ISBN/ISSN

9781108377751

Classification

NONE

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

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Subject(s)

Mathematics, Number Theory, Algebra

Specific Detail Info

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Statement of Responsibility

Pierre Guillot

Other Information

Cataloger

Arin

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Digital Object Identifier (DOI)

https://doi.org/10.1017/9781108377751

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