A gentle course in local class field theory : local number fields, Brauer groups, Galois cohomology [E-Book] / Pierre Guillot.
Guillot, Pierre, (author)
Cambridge : Cambridge University Press, 2018
1 online resource (xiv, 293 pages)
englisch
9781108377751
9781108421775
9781108432245
Full Text
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.