ISBN 9783843948906

978-3-8439-4890-6, Reihe Mathematik

Aslam Ali
Computations in Galois Cohomology

153 Seiten, Dissertation Technische Universität Kaiserslautern (2021), Softcover, A5

Zusammenfassung / Abstract

Cohomology groups of Galois extensions have many important applications in algebraic number theory. We compute the canonical generator of the second cohomology group of Galois extension L/K and then use this generator to construct a group extension. For local Galois extension, the key step to compute the canonical generator is to solve a norm equation. We develop efficient algorithms to solve the norm equations by using logarithms to convert it to a trace equations. We apply the canonical generator in Shafarevich theorem of local class field theory to determine the Galois group of an Eisenstein polynomial f. we discuss an efficient way to compute the norm group of large degree extensions which will be used to compute the Galois group. We also extend an algorithm to compute the canonical generator for Galois extension of number fields and use it to compute the Galois group.