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Identifier 000451313
Title Το Τοπικό-Γενικό Αξίωμα στη θεωρία αριθμών
Alternative Title The local-global principle in number theory
Author Καρτσάκη, Ευαγγελία
Thesis advisor Αντωνιάδης, Ιωάννης
Abstract In this thesis, we study the Hasse-Minkowski theorem (local - global principle), as well as the historical counterexamples. In the first chapter, we describe the process of contruction of the p-adic fields and study their algebraic and topological properties. Extremely important is Hensel’s Lemma which we use to prove the existence of local solutions of diophantine equations (solutions over p-adic fields), as well as the Hilbert sumbol and it’s properties, that we use to study quadratic forms over p-adic fields. In the second chapter, we develop concepts of quadratic forms theory used in the proof of Hasse-Minkowski theorem. Extremely useful are Witt’s theorems as well as theorems concerning quadratic forms over p-adic fields. Finally, in the third chapter, we study diophantine equations, for which the local global principle fails.
Language Greek, English
Subject Guadratic forms
Τετραγωνικές μορφές
Issue date 2022-07-22
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
  Type of Work--Post-graduate theses
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