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The Kronecker-Weber Theorem
dc.contributor | Quer Bosor, Jordi |
dc.contributor.author | Fulton Arrufat, Damià |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2018-09-10T11:01:35Z |
dc.date.available | 2018-09-10T11:01:35Z |
dc.date.issued | 2018-07 |
dc.identifier.uri | http://hdl.handle.net/2117/120978 |
dc.description.abstract | In this bachelor's thesis we give a complete proof of the Kronecker-Weber theorem, which states that every finite abelian extension over the field of rational numbers Q is contained in some cyclotomic extension of Q. We prove it using a local-global principle: the K-W theorem is true for Q if and only if its is true for Qp, the field of p-adic numbers, for every prime p; and then we prove the local case. In order to show this local-global principle, we study the p-adic fields Qp and their finite extensions, and characterize them as completions of number fields. |
dc.language.iso | eng |
dc.publisher | Universitat Politècnica de Catalunya |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
dc.subject.lcsh | Algebraic number theory |
dc.subject.other | Galois theory |
dc.subject.other | Number theory |
dc.subject.other | P-adic |
dc.subject.other | Local-global |
dc.title | The Kronecker-Weber Theorem |
dc.type | Bachelor thesis |
dc.subject.lemac | Cossos locals (Geometria algèbrica) |
dc.subject.lemac | Nombres, Teoria algebraica de |
dc.subject.ams | Classificació AMS::11 Number theory::11S Algebraic number theory: local and $p$-adic fields |
dc.identifier.slug | FME-1296 |
dc.rights.access | Open Access |
dc.date.updated | 2018-07-14T05:22:52Z |
dc.audience.educationlevel | Grau |
dc.audience.mediator | Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística |
dc.audience.degree | GRAU EN MATEMÀTIQUES (Pla 2009) |