Galois Representation

Please enable javascript in your browser.

Shafaeiabr, Masoud | 2015

2277 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 48818 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Rastgar, Arash; Rajaei, Ali
Abstract:
Let K, k be two fields and GK be the Galois group of separable closure of K. By a Galois representation of dimension n of GK we mean a homomorphism ρ : GK → GLn(k) of topological groups. In this thesis we want to introduce the theory of Galois representations according to the Taylor’s paper [20] which has written based on his speech in international mathematical conference (ICM 2004). In general we want to build a suitable background for the reader who wants to read the Taylor’s paper with presenting the concepts related to Galois representations such as p-adic and l-adic representations, geometric representations, modular forms, L-function of a Galois representation, Weil-Deligne representations and... As a special case, we will study elliptic curves and we will prove that the Galois representation of an elliptic curve E is unramified at the primes which E has a good reduction modulo them.
Keywords:
L-Function ; Cohomology Group ; Topological Group ; Galois Representations ; L-Adic Representation