Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini
Annales scientifiques de l'École Normale Supérieure (2003)
- Volume: 36, Issue: 6, page 977-1002
- ISSN: 0012-9593
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topKahn, Bruno. "Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini." Annales scientifiques de l'École Normale Supérieure 36.6 (2003): 977-1002. <http://eudml.org/doc/82624>.
@article{Kahn2003,
author = {Kahn, Bruno},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {fre},
number = {6},
pages = {977-1002},
publisher = {Elsevier},
title = {Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini},
url = {http://eudml.org/doc/82624},
volume = {36},
year = {2003},
}
TY - JOUR
AU - Kahn, Bruno
TI - Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2003
PB - Elsevier
VL - 36
IS - 6
SP - 977
EP - 1002
LA - fre
UR - http://eudml.org/doc/82624
ER -
References
top- [1] André Y., Cycles de Tate et cycles motivés sur les variétés abéliennes en caractéristique p>0, prépublication, 2003.
- [2] André Y., Kahn B., Nilpotence, radicaux et structures monoïdales (avec un appendice de Peter O'Sullivan), Rend. Sem. Math. Univ. Padova108 (2002) 107-291. Zbl1165.18300MR1956434
- [3] Beilinson A.A., Height pairings between algebraic cycles, in: Lect. Notes in Math., vol. 1289, Springer, 1987, pp. 1-26. Zbl0651.14002MR902590
- [4] Bloch S., Torsion algebraic cycles and a theorem of Roǐtman, Compositio Math.39 (1979) 107-127. Zbl0463.14002MR539002
- [5] Bloch S., Algebraic cycles and higher K-theory, Adv. Math.61 (1986) 267-304. Zbl0608.14004MR852815
- [6] Bloch S., Algebraic cycles and the Beĭlinson conjectures, in: The Lefschetz Centennial Conference (Mexico City, 1984), Contemp. Math., vol. 58(I), Amer. Math. Society, Providence, RI, 1986, pp. 65-79. Zbl0605.14017MR860404
- [7] Bloch S., The moving lemma for higher Chow groups, J. Alg. Geom.3 (1994) 537-568. Zbl0830.14003MR1269719
- [8] Bloch S., Lichtenbaum S., A spectral sequence for motivic cohomology, prépublication, 1996.
- [9] Colliot-Thélène J.-L., Sansuc J.-J., Soulé C., Torsion dans le groupe de Chow de codimension 2, Duke Math. J.50 (1983) 763-801. Zbl0574.14004MR714830
- [10] Colliot-Thélène J.-L., Hoobler R.T., Kahn B., The Bloch–Ogus–Gabber theorem, in: Fields Institute for Research in Mathematical Sciences Communications Series, vol. 16, Amer. Math. Society, Providence, RI, 1997, pp. 31-94. Zbl0911.14004MR1466971
- [11] Deligne P., La conjecture de Weil, I, Publ. Math. IHÉS43 (1974) 5-77. MR340258
- [12] Deligne P., Katz N., Groupes de Monodromie en géométrie algébrique (SGA 7) II, Lect. Notes in Math., vol. 340, Springer, 1973. Zbl0258.00005MR354657
- [13] Deligne P. et al. , Cohomologie étale (SGA 4 1/2), in: Lect. Notes in Math., vol. 569, Springer, 1977. Zbl0349.14008MR463174
- [14] Friedlander E., Suslin A., The spectral sequence relating algebraic K-theory and motivic cohomology, Ann. Sci. Éc. Norm. Sup.35 (2002) 773-875. Zbl1047.14011MR1949356
- [15] Gabber O., Sur la torsion dans la cohomologie l-adique d'une variété, C. R. Acad. Sci. Paris297 (1983) 179-182. Zbl0574.14019MR725400
- [16] Geisser T., Tate's conjecture, algebraic cycles and rational K-theory in characteristic p, 13 (1998) 109-122. Zbl0896.19001MR1611623
- [17] Geisser T., Weil-étale motivic cohomology, prépublication, 2002 , http://www.math.uiuc.edu/K-theory#565.
- [18] Geisser T., Levine M., The K-theory of fields in characteristic p, Invent. Math.139 (2000) 459-493. Zbl0957.19003MR1738056
- [19] Geisser T., Levine M., The Bloch–Kato conjecture and a theorem of Suslin–Voevodsky, J. Reine Angew. Math.530 (2001) 55-103. Zbl1023.14003MR1807268
- [20] Gillet H., Riemann–Roch theorems for higher algebraic K-theory, Adv. Math.40 (1981) 203-289. Zbl0478.14010MR624666
- [21] Gillet H., Gersten's conjecture for the K-theory with torsion coefficients of a discrete valuation ring, J. Algebra103 (1986) 377-380. Zbl0594.13014MR860713
- [22] Grayson D., Finite generation of the K-groups of a curve over a finite field (after D. Quillen), in: Lect. Notes in Math., vol. 966, Springer, 1982, pp. 69-90. Zbl0502.14004MR689367
- [23] Harder G., Die Kohomologie S-arithmetischer Gruppen über Funktionenkörpern, Invent. Math.42 (1977) 135-175. Zbl0391.20036MR473102
- [24] Izhboldin O., On p-torsion in KM∗ for fields of characteristic p, in: Algebraic K-Theory, Soviet Math., vol. 4, Amer. Math. Society, Providence, RI, 1991, pp. 129-144. Zbl0746.19002
- [25] Jannsen U., Continuous étale cohomology, Math. Ann.280 (1988) 207-245. Zbl0649.14011MR929536
- [26] Jannsen U., Motives, numerical equivalence and semi-simplicity, Invent. Math.107 (1992) 447-452. Zbl0762.14003MR1150598
- [27] de Jeu R., On K4(3) of curves over number fields, Invent. Math.125 (1996) 523-556. Zbl0864.11059MR1400316
- [28] de Jong A.J., Smoothness, semi-stability and alterations, Publ. Math. IHÉS83 (1996) 51-93. Zbl0916.14005MR1423020
- [29] Kahn B., K3 d'un schéma régulier, C. R. Acad. Sci. Paris315 (1992) 433-436. Zbl0790.14007MR1179052
- [30] Kahn B., Deux théorèmes de comparaison en cohomologie étale ; applications, Duke Math. J.69 (1993) 137-165. Zbl0789.14014MR1201695
- [31] Kahn B., Résultats de “pureté” pour les variétés lisses sur un corps fini, in: Algebraic K-Theory and Algebraic Topology, NATO ASI Series, Ser. C, vol. 407, Kluwer, 1993, pp. 57-62. Zbl0885.19003
- [32] Kahn B., Applications of weight-two motivic cohomology, Doc. Math.1 (1996) 395-416. Zbl0883.19002MR1423901
- [33] Kahn B., A sheaf-theoretic reformulation of the Tate conjecture, prépublication de l'Institut de Mathématiques de Jussieu no 150, 1998 , math.AG/9801017.
- [34] Kahn B., K-theory of semi-local rings with finite coefficients and étale cohomology, 25 (2002) 99-139. Zbl1013.19001MR1906669
- [35] Kahn B., The Geisser–Levine method revisited and algebraic cycles over a finite field, Math. Ann.324 (2002) 581-617. Zbl1014.14004MR1938459
- [36] Kahn B., Some finiteness results for étale cohomology, J. Number Theory99 (2002) 57-73. Zbl1055.14018MR1957244
- [37] Katsura T., Shioda T., On Fermat varieties, Tôhoku Math. J.31 (1979) 97-115. Zbl0415.14022MR526513
- [38] Katz N., Messing W., Some consequences of the Riemann hypothesis for varieties over finite fields, Invent. Math.23 (1974) 73-77. Zbl0275.14011MR332791
- [39] Kimura S.I., Chow motives can be finite-dimensional, in some sense, J. Alg. Geom., à paraître.
- [40] Kratzer C., λ-structure en K-théorie algébrique, Comment. Math. Helv.55 (1970) 233-254. Zbl0444.18008
- [41] Lenstra H.W., Zarhin Y.G., The Tate conjecture for almost ordinary abelian varieties over finite fields, in: Advances in Number Theory (Kingston, ON, 1991), Oxford Univ. Press, 1993, pp. 179-194. Zbl0817.14022MR1368419
- [42] Levine M., K-theory and motivic cohomology of schemes, I, prépublication, 2001.
- [43] Lichtenbaum S., Values of zeta functions at non-negative integers, in: Lect. Notes in Math., vol. 1068, Springer, 1984, pp. 127-138. Zbl0591.14014MR756089
- [44] Lichtenbaum S., The Weil-étale topology, prépublication, 2001.
- [45] Merkurjev A., Suslin A., K-cohomologie des variétés de Severi–Brauer et homomorphisme de reste normique, Izv. Akad. Nauk SSSR46 (1982) 1011-1046, (en russe), Trad. anglaise , Math. USSR Izvestiya21 (1983) 307-340. Zbl0525.18008
- [46] Merkurjev A.S., Suslin A.A., Le groupe K3 pour un corps, Izv. Akad. Nauk SSSR54 (1990) 339-356, (en russe), Trad. anglaise , Math. USSR Izv.36 (1990) 541-565. Zbl0725.19003
- [47] Milne J.S., Etale Cohomology, Princeton Univ. Press, Princeton, 1980. Zbl0433.14012MR559531
- [48] Milne J.S., Values of zeta functions of varieties over finite fields, Amer. J. Math.108 (1986) 297-360. Zbl0611.14020MR833360
- [49] Milne J.S., Motivic cohomology and values of the zeta function, Compositio Math.68 (1988) 59-102. Zbl0681.14007MR962505
- [50] Milne J.S., Motives over finite fields, in: Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., vol. 55(1), Amer. Math. Society, Providence, RI, 1994, pp. 401-459. Zbl0811.14018MR1265538
- [51] Milne J.S., Lefschetz motives and the Tate conjecture, Compositio Math.117 (1999) 47-81. Zbl0985.14010MR1692999
- [52] Milne J.S., The Tate conjecture for certain abelian varieties over finite fields, Acta Arith.100 (2001) 135-166. Zbl1047.11057MR1864152
- [53] Milne J.S., Ramachandran N., Integral motives and special values of zeta functions, prépublication, 2002 (version préliminaire) , math.NT/0204065.
- [54] Quillen D., On the cohomology and the K-theory of the general linear group over a finite field, Ann. of Math.96 (1972) 179-198. Zbl0355.18018MR315016
- [55] Raskind W., A finiteness theorem in the Galois cohomology of algebraic number fields, Trans. Amer. Math. Soc.303 (1987) 743-749. Zbl0648.12009MR902795
- [56] Rost M., Chow groups with coefficients, Doc. Math.1 (1996) 319-393. Zbl0864.14002MR1418952
- [57] Soulé C., Groupes de Chow et K-théorie de variétés sur un corps fini, Math. Ann.268 (1984) 317-345. Zbl0573.14001MR751733
- [58] Soulé C., Opérations en K-théorie algébrique, Can. Math. J.37 (1985) 488-550. Zbl0575.14015MR787114
- [59] Spiess M., Proof of the Tate conjecture for products of elliptic curves over finite fields, Math. Ann.314 (1999) 285-290. Zbl0941.11026MR1697446
- [60] Suslin A., Algebraic K-theory of fields, in: Proceedings of the International Congress of Mathematicians, Berkeley, 1986, pp. 222-244. Zbl0675.12005MR934225
- [61] Tate J.T., Algebraic cycles and poles of zeta functions, in: Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963), 1965, pp. 93-110. Zbl0213.22804MR225778
- [62] Tate J.T., Endomorphisms of abelian varieties over finite fields, Invent. Math.2 (1966) 134-144. Zbl0147.20303MR206004
- [63] Tate J.T., Conjectures on algebraic cycles in l-adic cohomology, in: Motives, Proc. Symposia Pure Math., vol. 55(1), Amer. Math. Society, Providence, RI, 1994, pp. 71-83. Zbl0814.14009MR1265523
- [64] Voevodsky V., Motivic cohomology with Z/2 coefficients, Publ. Math. IHÉS, à paraître. Zbl1057.14028
- [65] Weil A., Courbes algébriques et variétés abéliennes, Hermann, 1954, rééd. 1971. Zbl0208.49202
- [66] Zarhin Y.G., Abelian varieties of K3 type, in: Séminaire de théorie des nombres, Paris, 1990–1991, Progr. Math., vol. 108, Birkhäuser, 1992, pp. 263-279. Zbl0827.14031MR1263531
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