On the averaged Colmez conjecture

Xinyi Yuan; Shou Wu Zhang

doi:10.4007/annals.2018.187.2.4

On the averaged Colmez conjecture

Xinyi Yuan, Shou Wu Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

The Colmez conjecture is a formula expressing the Faltings height of an abelian variety with complex multiplication in terms of some linear combination of logarithmic derivatives of Artin L-functions. The aim of this paper to prove an averaged version of the conjecture, which was also proposed by Colmez.

Original language	English (US)
Pages (from-to)	533-638
Number of pages	106
Journal	Annals of Mathematics
Volume	187
Issue number	2
DOIs	https://doi.org/10.4007/annals.2018.187.2.4
State	Published - Mar 1 2018

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Arithmetic intersection
Colmez conjecture
Complex multiplication
Faltings height
L-function
Shimura curve

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10.4007/annals.2018.187.2.4

Cite this

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title = "On the averaged Colmez conjecture",

abstract = "The Colmez conjecture is a formula expressing the Faltings height of an abelian variety with complex multiplication in terms of some linear combination of logarithmic derivatives of Artin L-functions. The aim of this paper to prove an averaged version of the conjecture, which was also proposed by Colmez.",

keywords = "Arithmetic intersection, Colmez conjecture, Complex multiplication, Faltings height, L-function, Shimura curve",

author = "Xinyi Yuan and Zhang, {Shou Wu}",

note = "Publisher Copyright: {\textcopyright} 2018 Department of Mathematics, Princeton University.",

year = "2018",

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KW - Arithmetic intersection

KW - Colmez conjecture

KW - Complex multiplication

KW - Faltings height

KW - L-function

KW - Shimura curve

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JF - Annals of Mathematics

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On the averaged Colmez conjecture

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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