A New Northcott Property for Faltings Height
In 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...
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| creator | Mocz, Lucia |
| description | In 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. |
| doi_str_mv | 10.48550/arxiv.1709.06098 |
| format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.1709.06098</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry ; Mathematics - Number Theory</subject><creationdate>2017-09</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1709.06098$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1709.06098$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Mocz, Lucia</creatorcontrib><title>A New Northcott Property for Faltings Height</title><description>In 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
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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.</abstract><doi>10.48550/arxiv.1709.06098</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Geometry Mathematics - Number Theory |
| title | A New Northcott Property for Faltings Height |
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