num_pages: 0
description: Galois modules over local and global fields form the main subject of this monograph which can serve both as a textbook for students and as a reference book for the working mathematician on cohomological topics in number theory. The first part provides the necessary algebraic background. The arithmetic part deals with Galois groups of local and global local Tate duality the structure of the absolute Galois group of a local field extensions of global fields with restricted ramification cohomology of the idle and the idle class groups Poitou-Tate duality for finitely generated Galois modules the Hasse principle the theorem of Grunwald-Wang Leopoldt's conjecture Riemann's existence theorem for number fields embedding problems the theorems of Iwasawa and of Safarevic on solvable groups as Galois groups over global fields Iwasawa theory of local and global number fields and the characterization of number fields by their absolute Galois groups.
language: English
title: Cohomology of Number Fields
publisher: Springer