Schinck, Amélie (2001) The local-global principle in number theory. Masters thesis, Concordia University.
" 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)|
|Pagination:||vii, 72 leaves ; 29 cm.|
|Degree Name:||Theses (M.Sc.)|
|Program:||Mathematics and Statistics|
|Thesis Supervisor(s):||Kisilevsky, Hershy|
|Deposited By:||Concordia University Libraries|
|Deposited On:||27 Aug 2009 17:19|
|Last Modified:||08 Dec 2010 15:21|
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