Height pairings for algebraic cycles on abelian varieties
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 34 (2001) no. 4, pp. 503-523.
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     title = {Height pairings for algebraic cycles on abelian varieties},
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Künnemann, Klaus. Height pairings for algebraic cycles on abelian varieties. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 34 (2001) no. 4, pp. 503-523. doi : 10.1016/s0012-9593(01)01068-0. http://www.numdam.org/articles/10.1016/s0012-9593(01)01068-0/

[1] Beilinson A.A., Height pairings between algebraic cycles, in: Manin Yu.I. (Ed.), K-theory, Arithmetic and Geometry, Moscow 1984-86, Lect. Notes Math., 1289, Springer, Berlin, 1987, pp. 1-25, and Contemp. Math. 67 (1987) 1-24. | Zbl

[2] Bloch S., Height pairings for algebraic cycles, J. Pure Appl. Algebra 34 (1984) 119-145. | MR | Zbl

[3] Bloch S., Gillet H., Soulé C., Cycles on degenerate fibers, in: Arithmetic Geometry (Cortona, 1994), Sympos. Math. XXXVII, Cambridge Univ. Press, Cambridge, 1997, pp. 45-69. | MR | Zbl

[4] Deligne P., La conjecture de Weil II, Publ. Math. I.H.E.S. 52 (1981) 313-428. | Numdam | MR | Zbl

[5] Faltings G., Chai C.-L., Degenerations of Abelian Varieties, Springer, Berlin, 1990. | MR | Zbl

[6] Fulton W., Macpherson R., Sottile F., Sturmfels B., Intersection theory on spherical varieties, J. Algebraic Geometry 4 (1995) 181-193. | MR | Zbl

[7] Fulton W., Intersection Theory, Springer, Berlin, 1984. | MR | Zbl

[8] Fulton W., Introduction to Toric Varieties, Annals of Mathematics Studies, 131, Princeton University Press, Princeton, NJ, 1993. | MR | Zbl

[9] Gillet H., Soulé C., Intersection theory using Adams operations, Invent. Math. 90 (1987) 243-278. | MR | Zbl

[10] Gillet H., Soulé C., Arithmetic intersection theory, Publ. Math. I.H.E.S. 72 (1990) 94-174. | Numdam | MR | Zbl

[11] Künnemann K., Higher Picard varieties and the height pairing, Amer. J. Math. 118 (1996) 781-797. | MR | Zbl

[12] Künnemann K., Projective regular models for abelian varieties, semi-stable reduction, and the height pairing, Duke Math. J. 95 (1998) 161-212. | MR | Zbl

[13] Künnemann K., The Kähler identity for bigraded Hodge-Lefschetz modules and its application in non-archimedean Arakelov geometry, J. Algebraic Geometry 7 (1998) 651-672. | Zbl

[14] Künnemann K., Algebraic cycles on toric fibrations over abelian varieties, Math. Z. 232 (1999) 427-435. | MR | Zbl

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