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AuthorSteck, Christiandc.contributor.author
Date of accession2018-02-06T11:17:30Zdc.date.accessioned
Available in OPARU since2018-02-06T11:17:30Zdc.date.available
Year of creation2017dc.date.created
Date of first publication2018-02-06dc.date.issued
AbstractIn this thesis we study the resolution of cyclic quotient singularities on fibered surfaces, i.e. given a cyclic quotient X, we are concerned with finding a regular modification X of X. This is done by adapting the classical Hirzebruch–Jung resolution procedure to the arithmetic setting. We show that, under mild assumptions and after an étale extension, a resolution of Hirzebruch–Jung type exists and we provide an explicit construction. As an application we consider curves over a local field that admit a semistable regular model Y after a finite tame Galois extension with Galois group G. We show that the singularities of Y/G are always cyclic quotient singularities and that they fulfill the necessary prerequisites to apply our Hirzebruch–Jung resolution procedure. Further, we use this theory to obtain the classical Kodaira classification of elliptic curves that have good reduction after a finite tame extension.dc.description.abstract
Languageen_USdc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandarddc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v3dc.rights.uri
KeywordZyklischer Quotientdc.subject
KeywordHirzebruch-Jung Auflösungdc.subject
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHSingularities (Mathematics)dc.subject.lcsh
LCSHGeometry, algebraicdc.subject.lcsh
LCSHArithmetical algebraic geometrydc.subject.lcsh
TitleResolution of tame cyclic quotient singularities on fibered surfacesdc.title
Resource typeDissertationdc.type
Date of acceptance2017-12-20dcterms.dateAccepted
RefereeWewers, Stefandc.contributor.referee
RefereeSijsling, Jeroendc.contributor.referee
DOIhttp://dx.doi.org/10.18725/OPARU-5424dc.identifier.doi
PPN1013674499dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-oparu-5481-0dc.identifier.urn
GNDAuflösung von Singularitätendc.subject.gnd
GNDAlgebraische Geometriedc.subject.gnd
GNDArithmetische Geometriedc.subject.gnd
GNDArithmetische Flächedc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
InstitutionInstitut für Reine Mathematikuulm.affiliationSpecific
Grantor of degreeFakultät für Mathematik und Wirtschaftswissenschaftenuulm.thesisGrantor
DCMI TypeTextuulm.typeDCMI
CategoryPublikationenuulm.category
University Bibliographyjauulm.unibibliographie


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