Erratum to: “On the averaged Colmez conjecture”. (English) Zbl 1523.11106

Summary: We will fix an error in our paper [ibid. 187, No. 2, 533–638 (2018; Zbl 1412.11078)] on the average Colmez conjecture by proving a slightly weaker statement than Theorem 2.7, which is sufficient for application to the main results.


11G15 Complex multiplication and moduli of abelian varieties
14G40 Arithmetic varieties and schemes; Arakelov theory; heights
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)


Zbl 1412.11078
Full Text: DOI


[1] Andreatta, Fabrizio; Goren, Eyal Z.; Howard, Benjamin; Madapusi Pera, Keerthi, Faltings heights of abelian varieties with complex multiplication, Ann. of Math. (2). Annals of Mathematics. Second Series, 187, 391-531 (2018) · Zbl 1464.11059 · doi:10.4007/annals.2018.187.2.3
[2] Bosch, Siegfried; L\"{u}tkebohmert, Werner; Raynaud, Michel, N\'{e}ron Models, Ergeb. Math. Grenzgeb., 21, x+325 pp. (1990) · Zbl 0705.14001 · doi:10.1007/978-3-642-51438-8
[3] Chai, Ching-Li; Conrad, Brian; Oort, Frans, Complex multiplication and lifting problems, Math. Surveys Monogr., 195, x+387 pp. (2014) · Zbl 1298.14001 · doi:10.1090/surv/195
[4] Kisin, Mark, Modularity of 2-adic {B}arsotti-{T}ate representations, Invent. Math.. Inventiones Mathematicae, 178, 587-634 (2009) · Zbl 1304.11043 · doi:10.1007/s00222-009-0207-5
[5] Kisin, Mark, Integral models for {S}himura varieties of abelian type, J. Amer. Math. Soc.. Journal of the Amer. Math. Soc., 23, 967-1012 (2010) · Zbl 1280.11033 · doi:10.1090/S0894-0347-10-00667-3
[6] Mocz, Lucia, A {N}ew {N}orthcott {P}roperty for {F}altings {H}eight, 127 pp. (2018)
[7] Vign\'{e}ras, Marie-France, Arithm\'{e}tique des Alg\`ebres de Quaternions, Lecture Notes in Math., 800, vii+169 pp. (1980) · Zbl 0422.12008 · doi:10.1007/BFb0091027
[8] Yuan, Xinyi; Zhang, Shou-Wu, On the averaged {C}olmez conjecture, Ann. of Math. (2). Annals of Mathematics. Second Series, 187, 533-638 (2018) · Zbl 1412.11078 · doi:10.4007/annals.2018.187.2.4
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