@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}, publisher = {Seminario Matematico of the University of Padua}, volume = {128}, year = {2012}, mrnumber = {3076831}, zbl = {1272.14021}, language = {en}, url = {http://www.numdam.org/item/RSMUP_2012__128__55_0/} }
TY - JOUR AU - Bost, Jean-Benoît AU - Freixas i Montplet, Gerard TI - Semi-abelian Schemes and Heights of Cycles in Moduli Spaces of abelian Varieties JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2012 SP - 55 EP - 90 VL - 128 PB - Seminario Matematico of the University of Padua UR - http://www.numdam.org/item/RSMUP_2012__128__55_0/ LA - en ID - RSMUP_2012__128__55_0 ER -
%0 Journal Article %A Bost, Jean-Benoît %A Freixas i Montplet, Gerard %T Semi-abelian Schemes and Heights of Cycles in Moduli Spaces of abelian Varieties %J Rendiconti del Seminario Matematico della Università di Padova %D 2012 %P 55-90 %V 128 %I Seminario Matematico of the University of Padua %U http://www.numdam.org/item/RSMUP_2012__128__55_0/ %G en %F RSMUP_2012__128__55_0
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. http://www.numdam.org/item/RSMUP_2012__128__55_0/
[1] Hauteurs et discrétude, Sém. Bourbaki, Exposé 825, Astérisque 245, pp. 141-166. | Numdam | MR | Zbl
,[2] Points entiers sur les surfaces arithmétiques, J. Reine Angew. Math. 531 (2001), pp. 201-235. | MR | Zbl
,[3] Hauteur de Faltings et hauteur de Néron-Tate du diviseur thêta, Compos. Math. 142 (2006), pp. 1451-1458. | MR | Zbl
,[4] Letter to Ulf Kühn.
,[5] Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7 (1994), pp. 903-1027. | MR | Zbl
- - ,[6] Cohomological arithmetic Chow rings, J. Inst. Math. Jussieu 6 (2007), pp. 1-172. | MR | Zbl
- - ,[7] Arithmetic characteristic classes of automorphic vector bundles, Documenta Math. 10 (2005), pp. 619-716. | MR | Zbl
- - ,[8] Théorie de Hodge. II, Institut des Hautes É tudes Scientifiques. Publications Mathématiques, 40 (1971), pp. 5-57. | Numdam | MR | Zbl
,[9] Les schémas de modules de courbes elliptiques, Lecture Notes in Math. 349 (Springer, 1973), pp. 143-316. | MR | Zbl
- ,[10] Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math. 92 (1988), pp. 73-90. | MR | Zbl
,[11] Arakelov's theorem for abelian varieties, Invent. Math. 73 (1983), pp. 337-347. | MR | Zbl
,[12] Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), pp. 349-366. | MR | Zbl
,[13] Finiteness theorems for abelian varieties over number fields, Arithmetic Geometry (G. Cornell and J. H. Silverman, eds.), Springer-Verlag, 1986, pp. 9-27. | MR | Zbl
,[14] Degeneration of abelian varieties, Springer-Verlag, Berlin, 1990. | MR | Zbl
- ,[15] Rational points, Aspects of Mathematics, Vol. E6, Vieweg, 1984. | MR | Zbl
- et al.,[16] G. Freixas i Montplet, Heights and metrics with logarithmic singularities, J. Reine Angew. Math. 627 (2009), pp. 97-153. | MR | Zbl
[17] Technique de descente et théorèmes d'existence en géométrie algébrique, III, Sém. Bourbaki, Exposé 212, 1961. | Numdam | Zbl
,[18] On extending families of curves, J. Alg. Geom. 6 (1997), pp. 545-562. | MR | Zbl
- ,[19] The Faltings-Moriwaki modular height and isogenies of elliptic curves, J. Math. Kyoto. Univ. 48 (2008), pp. 661-682. | MR
,[20] Arakelov type inequalities for Hodge bundles over algebraic varieties, Part I: Hodge bundles over algebraic curves, J. Alg. Geom. 11 (2002), pp. 535-546. | MR | Zbl
- ,[21] Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables, Mém. Soc. Math. France, 80, SMF (2000). | Numdam | Zbl
,[22] Pinceaux de variétés abéliennes, Astérisque 129 (1985). | Numdam | MR | Zbl
,[23] Groupes de Picard et problèmes de Skolem. I, Ann. Scient. É c. Norm. Sup. 22 (1989), pp. 161-179 | Numdam | MR | Zbl
,[24] The modular height of an abelian variety and its finiteness property, Adv. Stud. Pure Math. 45 (2006), pp. 157-187. | MR | Zbl
,[25] Hirzebruch's Proportionality Theorem in the Non-Compact Case, Invent. Math. 42 (1977), pp. 239-272. | MR | Zbl
,[26] Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents, J. Reine angew. Math. 590 (2006), pp. 67-88. | MR | Zbl
,[27] Faisceaux amples sur les schémas en groupes et les espaces homogènes, Lecture Notes in Mathematics 119, Springer-Verlag, 1970. | MR | Zbl
,[28] Maximal Orders, London Math. Soc. Monograph New Series, Oxford University Press, New York, 2003. | MR | Zbl
,[29] Arithmetic over the ring of all algebraic integers, J. Reine. angew. Math. 368 (1986), pp. 127-133. | MR | Zbl
,[30] Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell, Astérisque 127 (1985). | Numdam | MR | Zbl
,[31] Equirépartition des petits points, Invent. Math. 127 (1997), pp. 337-347. | MR | Zbl
- - ,[32] Endomorphisms of Abelian Varieties over Finite Fields, Invent. Math. 2 (1966), pp. 134-144. | MR | Zbl
,[33] p-divisible groups, in Proceedings of a Conference on Local Fields, Driebergen, Springer-Verlag, 1967. | MR | Zbl
,[34] Abelian varieties in characteristic , Math. Notes of the Academy of Sciences of the USSR, 19 (1976), pp. 240-244. | MR | Zbl
,[35] Endomorphisms of Abelian varieties over fields of finite characteristic, Math. USSR Izvestija, 9, No. 2 (1975), pp. 255-260. | Zbl
,[36] Positive line bundles on arithmetic varieties, J. Amer. Math. Soc. 8 (1995), pp. 187-221. | MR | Zbl
,