Algebraic cycles on abelian varieties and their decomposition
Bollettino dell'Unione Matematica Italiana (2004)
- Volume: 7-B, Issue: 1, page 231-240
- ISSN: 0392-4041
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topMarini, Giambattista. "Algebraic cycles on abelian varieties and their decomposition." Bollettino dell'Unione Matematica Italiana 7-B.1 (2004): 231-240. <http://eudml.org/doc/194963>.
@article{Marini2004,
abstract = {For an Abelian Variety $X$, the Künneth decomposition of the rational equivalence class of the diagonal $\Delta\subset X\times X$ gives rise to explicit formulas for the projectors associated to Beauville's decomposition (1) of the Chow ring $CH^\{\bullet\}(X)$, in terms of push-forward and pull-back of $m$-multiplication. We obtain a few simplifications of such formulas, see theorem (4) below, and some related results, see proposition (9) below.},
author = {Marini, Giambattista},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {231-240},
publisher = {Unione Matematica Italiana},
title = {Algebraic cycles on abelian varieties and their decomposition},
url = {http://eudml.org/doc/194963},
volume = {7-B},
year = {2004},
}
TY - JOUR
AU - Marini, Giambattista
TI - Algebraic cycles on abelian varieties and their decomposition
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/2//
PB - Unione Matematica Italiana
VL - 7-B
IS - 1
SP - 231
EP - 240
AB - For an Abelian Variety $X$, the Künneth decomposition of the rational equivalence class of the diagonal $\Delta\subset X\times X$ gives rise to explicit formulas for the projectors associated to Beauville's decomposition (1) of the Chow ring $CH^{\bullet}(X)$, in terms of push-forward and pull-back of $m$-multiplication. We obtain a few simplifications of such formulas, see theorem (4) below, and some related results, see proposition (9) below.
LA - eng
UR - http://eudml.org/doc/194963
ER -
References
top- BEAUVILLE, A., Sur l'anneau de Chow d'une varieté abélienne, Math. Ann., 273 (1986), 647-651. Zbl0566.14003MR826463
- BLOCH, S., Some Elementary Theorems about Algebraic cycles on Abelian Varieties, Inventiones Math., 37 (1976), 215-228. Zbl0371.14007MR429883
- DENINGER, C.- MURRE, J., Motivic decomposition of abelian schemes and the Fourier transform, J. Reine Angew. Math., 422 (1991), 201-219. Zbl0745.14003MR1133323
- JANNSEN, U., Equivalence relation on algebraic cycles, NATO Sci. Ser. C Math. Phys. Sci., 548 (2000). 225-260. Zbl0988.14003MR1744947
- GREEN, M.- MURRE, J.- VOISIN, C., Algebraic Cycles and Hodge Theory, Lecture Notes in Mathematics, 1594 (1993). MR1335238
- KÜNNEMANN, K., On the Chow Motive of an Abelian Scheme, Proceedings of Symposia in pure Mathematics, 55 (1994), 189-205. Zbl0823.14032MR1265530
- MUKAI, S., Duality between and with its applications to Picard Sheaves, Nagoya Math. J., 81 (1981), 153-175. Zbl0417.14036MR607081
- SAITO, S., Motives and filtrations on Chow groups, II, NATO Sci. Ser. C Math. Phys. Sci., 548 (2000), 321-346. Zbl0974.14006MR1744952
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