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A new Northcott property for Faltings height

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Abstract : The Faltings height is a useful invariant for addressing questions in arithmetic geometry. In his celebrated proof of the Mordell and Shafarevich conjectures, Faltings shows the Faltings height satisfies a certain Northcott property, which allows him to deduce his finiteness statements. 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 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 able to use these techniques to moreover develop new Colmez-type formulas for the Faltings height.

MSC Codes :
11G50 - Heights
11R04 - Algebraic numbers; rings of algebraic integers
12F05 - Algebraic extensions
14G40 - Arithmetic varieties and schemes; Arakelov theory; heights

    Information on the Video

    Language : English
    Available date : 30/05/2018
    Conference Date : 22/05/2018
    Subseries : Research talks
    arXiv category : Number Theory ; Algebraic Geometry
    Mathematical Area(s) : Algebraic & Complex Geometry ; Number Theory
    Format : MP4 (.mp4) - HD
    Video Time : 00:55:55
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2018-05-22_Mocz.mp4

Information on the Event

Event Title : Diophantine geometry / ​Géométrie diophantienne
Dates : 21/05/2018 - 25/05/2018
Event Year : 2018
Event URL : https://conferences.cirm-math.fr/1754.html

Citation Data

DOI : 10.24350/CIRM.V.19407903
Cite this video as: (2018). A new Northcott property for Faltings height. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19407903
URI : http://dx.doi.org/10.24350/CIRM.V.19407903

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