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    3. A Gentle Course in Local Class Field Theory: Local Number Fields, Brauer Groups, Galois Cohomology

    A Gentle Course in Local Class Field Theory: Local Number Fields, Brauer Groups, Galois Cohomology

    Posted By: arundhati
    Date: 27 Jul 2020 01:41:28
    A Gentle Course in Local Class Field Theory: Local Number Fields, Brauer Groups, Galois Cohomology

    Pierre Guillot, "A Gentle Course in Local Class Field Theory: Local Number Fields, Brauer Groups, Galois Cohomology"
    English | ISBN: 1108421776 | 2018 | 306 pages | PDF | 1428 KB

    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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