Lokalno-globalni princip

master's thesis

• Author: Ivona Mrkalj
• Mentor: Filip Najman (mentor)
• Committee member: Filip Najman (predsjednik povjerenstva)
• Committee member: Mirko Primc (član povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Tema ovog diplomskog rada je lokalno-globalni princip. Dokazati ćemo jednu od najznačajnijih posljedica lokalno-globalnog principa teorem Hasse-Minkowskog, koji tvrdi da lokalno globalni princip vrijedi za kvadratne forme. U prvom poglavlju ćemo se upoznati s osnovnim pojmovima i rezultatima teorije brojeva. U drugom i trećem poglavlju smo definirali p-adske brojeve i kvadratne forme, te dokazali teoreme i tvrdnje koje će biti od velike važnosti u dokazivanju teorema Hasse-Minkowski. Ovaj rad zaključiti ćemo s dokazom Hasse-Minkowski teorema, koji ćemo provoditi zasebno za kvadratne forme s 1,2,3,4 i više od 5 varijabli.

Abstract (english)

The theme of this master thesis is the local-global principle. We are going to prove one of the most significant results of the local-global principle the Hasse-Minkowski theorem, which claims that local-global principle is valid for quadratic forms. In the first chapter we are going to get familiar with basic terms and results of number theory. In the second and third chapter we define p-adic numbers and quadratic forms, and prove theorems and statements that will be of significant importance in proving the Hasse-Minkowski theorem. We will conclude this master thesis with a proof of the Hasse-Minkowski theorem, which we will conduct by proving it separately for quadratic forms with 1,2,3,4, and more than 5 variables.

• Keywords: lokalno-globalni princip; teorem Hasse-Minkowskog; kvadratne forme
• Keywords (english): local-global principle; Hasse-Minkowski theorem; quadratic forms
• Language: croatian
• URN:NBN: urn:nbn:hr:217:817121
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-25 12:54:40