Semi-abelian Schemes and Heights of Cycles in Moduli Spaces of abelian Varieties
Rendiconti del Seminario Matematico della Università di Padova, Tome 128 (2012), pp. 55-90 
@article{RSMUP_2012__128__55_0,
     author = {Bost, Jean-Beno{\^\i}t and Freixas i Montplet, Gerard},
     title = {Semi-abelian {Schemes} and {Heights} of {Cycles} in {Moduli} {Spaces} of abelian {Varieties}},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {55--90},
     year = {2012},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {128},
     mrnumber = {3076831},
     zbl = {1272.14021},
     language = {en},
     url = {https://www.numdam.org/item/RSMUP_2012__128__55_0/}
}
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Bost, Jean-Benoît; Freixas i Montplet, Gerard. Semi-abelian Schemes and Heights of Cycles in Moduli Spaces of abelian Varieties. Rendiconti del Seminario Matematico della Università di Padova, Tome 128 (2012), pp. 55-90. https://www.numdam.org/item/RSMUP_2012__128__55_0/

[1] A. Abbes, Hauteurs et discrétude, Sém. Bourbaki, Exposé 825, Astérisque 245, pp. 141-166. | Zbl | MR | Numdam

[2] P. Autissier, Points entiers sur les surfaces arithmétiques, J. Reine Angew. Math. 531 (2001), pp. 201-235. | Zbl | MR

[3] P. Autissier, Hauteur de Faltings et hauteur de Néron-Tate du diviseur thêta, Compos. Math. 142 (2006), pp. 1451-1458. | Zbl | MR

[4] J.-B. Bost, Letter to Ulf Kühn.

[5] J.-B. Bost - H. Gillet - C. Soulé, Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7 (1994), pp. 903-1027. | Zbl | MR

[6] J. I. Burgos - J. Kramer - U. Kühn, Cohomological arithmetic Chow rings, J. Inst. Math. Jussieu 6 (2007), pp. 1-172. | Zbl | MR

[7] J. I. Burgos - J. Kramer - U. Kühn, Arithmetic characteristic classes of automorphic vector bundles, Documenta Math. 10 (2005), pp. 619-716. | Zbl | MR

[8] P. Deligne, Théorie de Hodge. II, Institut des Hautes É tudes Scientifiques. Publications Mathématiques, 40 (1971), pp. 5-57. | Zbl | MR | Numdam

[9] P. Deligne - M. Rapoport, Les schémas de modules de courbes elliptiques, Lecture Notes in Math. 349 (Springer, 1973), pp. 143-316. | Zbl | MR

[10] W. Duke, Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math. 92 (1988), pp. 73-90. | Zbl | MR

[11] G. Faltings, Arakelov's theorem for abelian varieties, Invent. Math. 73 (1983), pp. 337-347. | Zbl | MR

[12] G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), pp. 349-366. | Zbl | MR

[13] G. Faltings, Finiteness theorems for abelian varieties over number fields, Arithmetic Geometry (G. Cornell and J. H. Silverman, eds.), Springer-Verlag, 1986, pp. 9-27. | Zbl | MR

[14] G. Faltings - C.-L. Chai, Degeneration of abelian varieties, Springer-Verlag, Berlin, 1990. | Zbl | MR

[15] G. Faltings - G. Wüstholz et al., Rational points, Aspects of Mathematics, Vol. E6, Vieweg, 1984. | Zbl | MR

[16] G. Freixas i Montplet, Heights and metrics with logarithmic singularities, J. Reine Angew. Math. 627 (2009), pp. 97-153. | Zbl | MR

[17] A. Grothendieck, Technique de descente et théorèmes d'existence en géométrie algébrique, III, Sém. Bourbaki, Exposé 212, 1961. | Zbl | Numdam

[18] A. J. De Jong - F. Oort, On extending families of curves, J. Alg. Geom. 6 (1997), pp. 545-562. | Zbl | MR

[19] H. Ikoma, The Faltings-Moriwaki modular height and isogenies of elliptic curves, J. Math. Kyoto. Univ. 48 (2008), pp. 661-682. | MR

[20] J. Jost - K. Zuo, Arakelov type inequalities for Hodge bundles over algebraic varieties, Part I: Hodge bundles over algebraic curves, J. Alg. Geom. 11 (2002), pp. 535-546. | Zbl | MR

[21] V. Maillot, Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables, Mém. Soc. Math. France, 80, SMF (2000). | Zbl | Numdam

[22] L. Moret-Bailly, Pinceaux de variétés abéliennes, Astérisque 129 (1985). | Zbl | MR | Numdam

[23] L. Moret-Bailly, Groupes de Picard et problèmes de Skolem. I, Ann. Scient. É c. Norm. Sup. 22 (1989), pp. 161-179 | Zbl | MR | Numdam

[24] A. Moriwaki, The modular height of an abelian variety and its finiteness property, Adv. Stud. Pure Math. 45 (2006), pp. 157-187. | Zbl | MR

[25] D. Mumford, Hirzebruch's Proportionality Theorem in the Non-Compact Case, Invent. Math. 42 (1977), pp. 239-272. | Zbl | MR

[26] H. Randriambololona, Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents, J. Reine angew. Math. 590 (2006), pp. 67-88. | Zbl | MR

[27] M. Raynaud, Faisceaux amples sur les schémas en groupes et les espaces homogènes, Lecture Notes in Mathematics 119, Springer-Verlag, 1970. | Zbl | MR

[28] I. Reiner, Maximal Orders, London Math. Soc. Monograph New Series, Oxford University Press, New York, 2003. | Zbl | MR

[29] R. Rumely, Arithmetic over the ring of all algebraic integers, J. Reine. angew. Math. 368 (1986), pp. 127-133. | Zbl | MR

[30] L. Szpiro, Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell, Astérisque 127 (1985). | Zbl | MR | Numdam

[31] L. Szpiro - E. Ullmo - S. Zhang, Equirépartition des petits points, Invent. Math. 127 (1997), pp. 337-347. | Zbl | MR

[32] J. Tate, Endomorphisms of Abelian Varieties over Finite Fields, Invent. Math. 2 (1966), pp. 134-144. | Zbl | MR

[33] J. Tate, p-divisible groups, in Proceedings of a Conference on Local Fields, Driebergen, Springer-Verlag, 1967. | Zbl | MR

[34] Y. G. Zarhin, Abelian varieties in characteristic p , Math. Notes of the Academy of Sciences of the USSR, 19 (1976), pp. 240-244. | Zbl | MR

[35] Y. G. Zarhin, Endomorphisms of Abelian varieties over fields of finite characteristic, Math. USSR Izvestija, 9, No. 2 (1975), pp. 255-260. | Zbl

[36] S. Zhang, Positive line bundles on arithmetic varieties, J. Amer. Math. Soc. 8 (1995), pp. 187-221. | Zbl | MR