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The local-global principle in number theory

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The local-global principle in number theory

Schinck, Amélie (2001) The local-global principle in number theory. Masters thesis, Concordia University.

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Abstract

" p-adic fields provide remarkable, easy and natural solutions to problems which apparently have no relation to p-adic fields and which otherwise can be resolved, if at all, only by deep and arduous methods ". -- J. W. S. Cassels The first Local-Global Principle, formulated by Hasse in 1921, relates the behaviour of rational quadratic forms in [Special characters omitted.] (global field) to their behaviour in the p -adic fields [Special characters omitted.] (local fields). The notion of using local information as a stepping stone towards understanding more difficult global properties has been generalized and applied to many problems, making Local-Global methods a powerful number theoretic tool. Even when the principle fails, we can sometimes salvage some connection between the local and the global. This thesis aims to give a survey of the basic theory.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Schinck, Amélie
Pagination:vii, 72 leaves ; 29 cm.
Institution:Concordia University
Degree Name:Theses (M.Sc.)
Program:Mathematics and Statistics
Date:2001
Thesis Supervisor(s):Kisilevsky, Hershy
ID Code:1489
Deposited By:Concordia University Libraries
Deposited On:27 Aug 2009 13:19
Last Modified:08 Dec 2010 10:21
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