Galois Cohomology and Class Field Theory (Universitext)

December 4, 2020
Galois Cohomology and Class Field Theory (Universitext)

This graduate textbook offers an introduction to modern methodsin number theory. It gives a complete account of the main resultsof class field theory as well as the Poitou-Tate duality theorems,considered crowning achievements of modern number theory.Assuming a first graduate course in algebra and number theory,the book begins with an introduction to group and Galoiscohomology. Local fields and local class field theory, includingLubin-Tate formal group laws, are covered next, followed by globalclass field theory and the description of abelian extensions ofglobal fields. The final part of the book gives an accessible yetcomplete exposition of the Poitou-Tate duality theorems. Twoappendices cover the necessary background in homological algebraand the analytic theory of Dirichlet L-series, including theČebotarev density theorem.Based on several advanced courses given by the author, thistextbook has been written for graduate students. Including completeproofs and numerous exercises, the book will also appeal to moreexperienced mathematicians, either as a text to learn the subjector as a reference.