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A Gentle Course in Local Class Field Theory

Pierre Guillot · ISBN 9781108421775
A Gentle Course in Local Class Field Theory | Zookal Textbooks | Zookal Textbooks
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Description

Publisher Cambridge University Press
Author(s) Pierre Guillot
Subtitle Local Number Fields, Brauer Groups, Galois Cohomology
Published 1st November 2018
Related course codes

Local Number Fields, Brauer Groups, Galois Cohomology

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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