Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini

Bruno Kahn

Annales scientifiques de l'École Normale Supérieure (2003)

  • Volume: 36, Issue: 6, page 977-1002
  • ISSN: 0012-9593

How to cite

top

Kahn, 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. [1] André Y., Cycles de Tate et cycles motivés sur les variétés abéliennes en caractéristique p&gt;0, prépublication, 2003. 
  2. [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. [3] Beilinson A.A., Height pairings between algebraic cycles, in: Lect. Notes in Math., vol. 1289, Springer, 1987, pp. 1-26. Zbl0651.14002MR902590
  4. [4] Bloch S., Torsion algebraic cycles and a theorem of Roǐtman, Compositio Math.39 (1979) 107-127. Zbl0463.14002MR539002
  5. [5] Bloch S., Algebraic cycles and higher K-theory, Adv. Math.61 (1986) 267-304. Zbl0608.14004MR852815
  6. [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. [7] Bloch S., The moving lemma for higher Chow groups, J. Alg. Geom.3 (1994) 537-568. Zbl0830.14003MR1269719
  8. [8] Bloch S., Lichtenbaum S., A spectral sequence for motivic cohomology, prépublication, 1996. 
  9. [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. [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. [11] Deligne P., La conjecture de Weil, I, Publ. Math. IHÉS43 (1974) 5-77. MR340258
  12. [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. [13] Deligne P. et al. , Cohomologie étale (SGA 4 1/2), in: Lect. Notes in Math., vol. 569, Springer, 1977. Zbl0349.14008MR463174
  14. [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. [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. [16] Geisser T., Tate's conjecture, algebraic cycles and rational K-theory in characteristic p, 13 (1998) 109-122. Zbl0896.19001MR1611623
  17. [17] Geisser T., Weil-étale motivic cohomology, prépublication, 2002 , http://www.math.uiuc.edu/K-theory#565. 
  18. [18] Geisser T., Levine M., The K-theory of fields in characteristic p, Invent. Math.139 (2000) 459-493. Zbl0957.19003MR1738056
  19. [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. [20] Gillet H., Riemann–Roch theorems for higher algebraic K-theory, Adv. Math.40 (1981) 203-289. Zbl0478.14010MR624666
  21. [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. [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. [23] Harder G., Die Kohomologie S-arithmetischer Gruppen über Funktionenkörpern, Invent. Math.42 (1977) 135-175. Zbl0391.20036MR473102
  24. [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. [25] Jannsen U., Continuous étale cohomology, Math. Ann.280 (1988) 207-245. Zbl0649.14011MR929536
  26. [26] Jannsen U., Motives, numerical equivalence and semi-simplicity, Invent. Math.107 (1992) 447-452. Zbl0762.14003MR1150598
  27. [27] de Jeu R., On K4(3) of curves over number fields, Invent. Math.125 (1996) 523-556. Zbl0864.11059MR1400316
  28. [28] de Jong A.J., Smoothness, semi-stability and alterations, Publ. Math. IHÉS83 (1996) 51-93. Zbl0916.14005MR1423020
  29. [29] Kahn B., K3 d'un schéma régulier, C. R. Acad. Sci. Paris315 (1992) 433-436. Zbl0790.14007MR1179052
  30. [30] Kahn B., Deux théorèmes de comparaison en cohomologie étale ; applications, Duke Math. J.69 (1993) 137-165. Zbl0789.14014MR1201695
  31. [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. [32] Kahn B., Applications of weight-two motivic cohomology, Doc. Math.1 (1996) 395-416. Zbl0883.19002MR1423901
  33. [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. [34] Kahn B., K-theory of semi-local rings with finite coefficients and étale cohomology, 25 (2002) 99-139. Zbl1013.19001MR1906669
  35. [35] Kahn B., The Geisser–Levine method revisited and algebraic cycles over a finite field, Math. Ann.324 (2002) 581-617. Zbl1014.14004MR1938459
  36. [36] Kahn B., Some finiteness results for étale cohomology, J. Number Theory99 (2002) 57-73. Zbl1055.14018MR1957244
  37. [37] Katsura T., Shioda T., On Fermat varieties, Tôhoku Math. J.31 (1979) 97-115. Zbl0415.14022MR526513
  38. [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. [39] Kimura S.I., Chow motives can be finite-dimensional, in some sense, J. Alg. Geom., à paraître. 
  40. [40] Kratzer C., λ-structure en K-théorie algébrique, Comment. Math. Helv.55 (1970) 233-254. Zbl0444.18008
  41. [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. [42] Levine M., K-theory and motivic cohomology of schemes, I, prépublication, 2001. 
  43. [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. [44] Lichtenbaum S., The Weil-étale topology, prépublication, 2001. 
  45. [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. [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. [47] Milne J.S., Etale Cohomology, Princeton Univ. Press, Princeton, 1980. Zbl0433.14012MR559531
  48. [48] Milne J.S., Values of zeta functions of varieties over finite fields, Amer. J. Math.108 (1986) 297-360. Zbl0611.14020MR833360
  49. [49] Milne J.S., Motivic cohomology and values of the zeta function, Compositio Math.68 (1988) 59-102. Zbl0681.14007MR962505
  50. [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. [51] Milne J.S., Lefschetz motives and the Tate conjecture, Compositio Math.117 (1999) 47-81. Zbl0985.14010MR1692999
  52. [52] Milne J.S., The Tate conjecture for certain abelian varieties over finite fields, Acta Arith.100 (2001) 135-166. Zbl1047.11057MR1864152
  53. [53] Milne J.S., Ramachandran N., Integral motives and special values of zeta functions, prépublication, 2002 (version préliminaire) , math.NT/0204065. 
  54. [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. [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. [56] Rost M., Chow groups with coefficients, Doc. Math.1 (1996) 319-393. Zbl0864.14002MR1418952
  57. [57] Soulé C., Groupes de Chow et K-théorie de variétés sur un corps fini, Math. Ann.268 (1984) 317-345. Zbl0573.14001MR751733
  58. [58] Soulé C., Opérations en K-théorie algébrique, Can. Math. J.37 (1985) 488-550. Zbl0575.14015MR787114
  59. [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. [60] Suslin A., Algebraic K-theory of fields, in: Proceedings of the International Congress of Mathematicians, Berkeley, 1986, pp. 222-244. Zbl0675.12005MR934225
  61. [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. [62] Tate J.T., Endomorphisms of abelian varieties over finite fields, Invent. Math.2 (1966) 134-144. Zbl0147.20303MR206004
  63. [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. [64] Voevodsky V., Motivic cohomology with Z/2 coefficients, Publ. Math. IHÉS, à paraître. Zbl1057.14028
  65. [65] Weil A., Courbes algébriques et variétés abéliennes, Hermann, 1954, rééd. 1971. Zbl0208.49202
  66. [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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.