On the averaged Colmez conjecture

Xinyi Yuan, Shou Wu Zhang

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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 languageEnglish (US)
Pages (from-to)533-638
Number of pages106
JournalAnnals of Mathematics
Issue number2
StatePublished - Mar 1 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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


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