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A New Northcott Property for Faltings Height

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datacite.rightsopen.access
dc.contributor.advisorZhang, Shouwu
dc.contributor.authorMocz, Lucia
dc.contributor.otherMathematics Department
dc.date.accessioned2018-06-12T17:39:59Z
dc.date.accessioned2026-09-30T11:31:29Z
dc.date.available2018-06-12T17:39:59Z
dc.date.available2026-09-30T11:31:29Z
dc.date.issued2018
dc.description.abstractIn this work we prove a new Northcott property for the Faltings height. Namely we show, assuming the Colmez Conjecture and the Artin Conjecture, that there are finitely many CM abelian varieties over the complex numbers of a fixed dimension which have bounded Faltings height. The technique developed uses new tools from integral p-adic Hodge theory to study the variation of Faltings height within an isogeny class of CM abelian varieties. In special cases, we are moreover able to use the technique to develop new Colmez-type formulas for the Faltings height.
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp011z40kw528
dc.identifier.urihttps://theses-dissertations.princeton.edu/handle/88435/dsp011z40kw528
dc.language.isoen
dc.publisherPrinceton, NJ : Princeton University
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: <a href=http://catalog.princeton.edu> catalog.princeton.edu </a>
dc.subjectArakelov Theory
dc.subjectArithmetic Geometry
dc.subjectFaltings Height
dc.subjectNumber Theory
dc.subject.classificationMathematics
dc.titleA New Northcott Property for Faltings Height
dc.typeAcademic dissertations (Ph.D.)
dspace.entity.typePublication
pu.projectgrantnumber690-2143

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