On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field

 Access to full text

 Full (PDF)

1. [A1] J. ALPERIN, Local Representation Theory (Cambridge studies in advanced math., Vol. 11, Cambridge University press, Cambridge, 1986). Zbl0593.20003MR87i:20002
2. [A-M] M. F. ATIYAH and I. G. MACDONALD, Introduction to Commutative Algebra, Addison-Wesley, Reading Mass., 1969. Zbl0175.03601MR39 #4129
3. [B] S. BLOCH, Algebraic cycles and values of L-functions (J. reine und angew. Math., Vol. 350, 1984, pp. 94-108). Zbl0527.14008MR85i:11052
4. [B1] S. BLOCH, Torsion algebraic cycles and a theorem of Roitman (Compositio Math. Vol. 39, 1979, pp. 107-127). Zbl0463.14002MR80k:14012
5. [B2] S. BLOCH, Algebraic cycles and values of L-functions II (Duke Math. J., Vol. 52, 1985, pp. 379-397). Zbl0628.14006MR87a:14021
6. [Be] A. BEAUVILLE, Le nombre minimum de fibres singulières d'une courbe stable sur P1, in Séminaire sur les pinceaux de courbes de genre au moins deux, L. Szpiro ed. (Astérisque, Vol. 86, 1981, pp. 97-108). Zbl0502.14009
7. [Be2] A. BEAUVILLE, Les familles stables de courbes elliptiques sur P1 admettant quatre fibres singulières (C.R. Acad. Sci., Paris, n° 294, 1982, pp. 657-660). Zbl0504.14016MR83h:14008
8. [Be3] A. BEAUVILLE, Le groupe de monodromie des familles universelles d'hypersurfaces et d'intersections complètes, in H. Grauert ed., Complex analysis and algebraic geometry. Proc. Conf., Goettingen 1985 (Lect. Notes Math., n° 1194, pp. 8-18, Springer, New York, 1986). Zbl0603.14011
9. [Bi-Ku] B. BIRCH and KUYK, ed., Modular functions of one variable IV (Lect. Notes Math., n° 476, 1972). Zbl0315.14014MR51 #12708
10. [Co-Ra] J.-L. COLLIOT-THÉLÈNE and W. RASKIND, K2-cohomology and the second Chow group (Math. Ann. n° 270, 1985, pp. 165-199). Zbl0536.14004MR86m:14005
11. [Co-S-S] J.-L. COLLIOT-THÉLÈNE, J.-J. SANSUC and C. SOULÉ, Torsion dans le groupe de Chow de codimension deux (Duke Math. J., Vol. 50, 1983, pp. 763-801). Zbl0574.14004MR85d:14010
12. [D] P. DELIGNE, Formes modulaires et représentations l-adiques (Séminaire Bourbaki n° 355, Lect. Notes in Math., Vol. 179, Springer Verlag, 1971, pp. 139-172). Zbl0206.49901
13. [D2] P. DELIGNE, Variétés abéliennes ordinaires sur un corps fini (Inv. math., Vol. 8, 1969, pp. 238-243). Zbl0179.26201MR40 #7270
14. [Fu] W. FULTON, Intersection Theory (Ergeb. Math. Grenzgeb., Vol. 2, Springer-Verlag, 1984). Zbl0541.14005MR85k:14004
15. [Gro] B. GROSS, Representation theory and the cuspidal group of X (p) (Duke Math. J., Vol. 54, 1987, pp. 67-75). Zbl0629.14021MR89b:11052
16. [Gr-D] A. GROTHENDIECK, rédigé par P. DELIGNE, La classe de cohomologie associée à un cycle (SGA 4 1/2, Lect. Notes Math., n° 569, 1977, pp. 129-153). Zbl0349.14012MR57 #3132
17. [Grot] A. GROTHENDIECK, Technique de descente et théorèmes d'existence en géométrie algébrique V. Les schémas de Picard : Théorèmes d'existence (Sém. Bourbaki n° 232, 1962). Zbl0238.14014
18. [Ha] B. HARRIS, Homological versus algebraic equivalence in a Jacobian (Proc. Nat. Acad. Sci. U.S.A., Vol. 80, 1983, pp. 1157-1158). Zbl0523.14006MR84m:14009
19. [Ja] U. JANNSEN, Mixed motives and algebraic K-theory (Lect. Notes Math., Vol. 1400, Berlin Heidelberg New York, Springer, 1990). Zbl0691.14001MR91g:14008
20. [La1] S. LANG, Sur les séries L d'une variété algébrique (Bull. Soc. Math. France, Vol. 84, 1956, pp. 385-407). Zbl0089.26301MR19,578c
21. [La2] S. LANG, Elliptic Functions, Addison-Wesley, London, 1973. Zbl0316.14001MR53 #13117
22. [Lau] G. LAUMON, Homologie étale, in Séminaire de géométrie analytique, A. Douady and J.-L. Verdier ed. (Astérisque, Vol. 36-377, 1976, pp. 163-188). Zbl0341.14006MR56 #3017
23. [Lig] G. LIGOZAT, Courbes Modulaires de Genre 1 (Bull. Soc. Math. France, Vol. 43, Paris, 1975). Zbl0322.14011MR54 #5121
24. [M-S] A. S. MERKUR'EV and A. A. SUSLIN, K-Cohomology of Severi-Brauer varieties and the norm residue homomorphism (Math. USSR Izvestiya, Vol. 21, 1983, pp. 307-340). Zbl0525.18008
25. [Mi] J. MILNE, Etale Cohomology, Princeton University Press, Princeton, 1980. Zbl0433.14012MR81j:14002
26. [Mi2] J. MILNE, Zero cycles on algebraic varieties in non-zero characteristic : Rojtman's theorem (Compositio Math., Vol. 47, 1982, pp. 271-287). Zbl0506.14006MR85b:14011
27. [Mi3] J. MILNE, Arithmetic Duality Theorems, Academic Press, Orlando, 1986. Zbl0613.14019MR88e:14028
28. [Mu] D. MUMFORD, Abelian Varieties, Oxford University Press, Oxford, 1970. Zbl0223.14022MR44 #219
29. [Ne] J. NEKOVÁŘ, Kolyvagin's method for Chow groups of Kuga-Sato varieties (Inv. Math., Vol. 107, 1992, pp. 99-125). Zbl0729.14004MR93b:11076
30. [Ogg] A. OGG, Elliptic curves and wild ramification (Amer. J. Math., Vol. 89, 1967, pp. 1-21). Zbl0147.39803MR34 #7509
31. [Ra] W. RASKIND, W., A finiteness theorem in the Galois Cohomology of algebraic number fields (Trans. AMS, Vol. 303, 1987, pp. 743-749). Zbl0648.12009MR88m:11098
32. [Ro] J. ROBERTS, Chow's moving lemma, in Algebraic Geometry, F. Oort ed., Wolters-Noordhoff Publ. Groningen, 1972, pp. 89-96. MR52 #3154
33. [Roi] A. A. ROITMAN, The torsion of the group of 0-cycles modulo rational equivalence (Ann. of Math., Vol. 111, 1980, pp. 553-569). Zbl0504.14006MR81g:14003
34. [Sch-BB] C. SCHOEN, Complex multiplication cycles and the conjecture of Beilinson and Bloch (Trans. A.M.S., Vol. 339, 1993, pp. 87-115). Zbl0811.14003MR93k:14011
35. [Sch-CM] C. SCHOEN, Complex multiplication cycles on elliptic modular threefolds (Duke Math J., Vol. 53, 1986, pp. 771-794). Zbl0623.14018MR87m:14041
36. [Sch-FP] C. SCHOEN, On fiber products of rational elliptic surfaces with section (Math. Z., Vol. 197, 1988, pp. 177-199). Zbl0631.14032MR89c:14062
37. [Sch-MR] C. SCHOEN, On certain modular representations in the cohomology of algebraic curves (J. of Algebra, Vol. 135, 1990, pp. 1-18). Zbl0727.20033MR91h:14021
38. [Sch-T] C. SCHOEN, Some examples of torsion in the Griffiths group (Math. Ann., Vol. 293, 1992, pp. 651-679). Zbl0790.14006MR94d:14009
39. [Se1] J. P. SERRE, Linear representations of finite groups (Graduate Texts in Math., Vol. 42, Springer-Verlag, New York, 1977). Zbl0355.20006MR56 #8675
40. [Se2] J. P. SERRE, Local Fields (Graduate Texts in Math., Vol. 67, Springer-Verlag, New York, 1979). Zbl0423.12016MR82e:12016
41. [Sh] G. SHIMURA, On elliptic curves with complex multiplication as factors of Jacobians of modular function fields (Nagoya Math. J., Vol. 43, 1971, pp. 199-208). Zbl0225.14015MR45 #5111
42. [Sh2] G. SHIMURA, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press, 1971. Zbl0221.10029
43. [Si1] J. SILVERMAN, The Arithmetic of elliptic curves, Springer Verlag, 1986. Zbl0585.14026MR87g:11070
44. [So] C. SOULÉ, Groupes de Chow et K-théorie de variétés sur un corps fini (Math. Ann., Vol. 268, 1984, pp. 317-345). Zbl0573.14001MR86k:14017
45. [St] J. STEENBRINK, Limits of Hodge structures (Invent. Math. Vol. 31, 1976, pp. 229-257). Zbl0303.14002MR55 #2894
46. [Ste] N. M. STEPHENS, The diophantine equation x3 + y3 = Dz3 and the conjectures of Birch and Swinnerton-Dyer (J. reine angew. Math., Vol. 231, 1968, pp. 121-162). Zbl0221.10023MR37 #5225
47. [Su] N. SUWA, Sur l'image de l'application d'Abel-Jacobi de Bloch (Bull. Soc. math. France, Vol. 116, 1988, pp. 69-101). Zbl0686.14006MR89j:14003
48. [Ta1] J. TATE, Relations between K2 and Galois cohomology (Invent. Math., Vol. 36, 1976, pp. 257-274). Zbl0359.12011MR55 #2847
49. [Ta2] J. TATE, Classes d'isogénie des variétés abéliennes sur un corps fini (d'après Honda) (Sém. Bourbaki, n° 352, 1968). Zbl0212.25702
50. [Ta3] J. TATE, Endomorphisms of Abelian Varieties (Inv. Math., Vol. 2, 1966, pp. 134-144). Zbl0147.20303MR34 #5829
51. [Wa] W. WATERHOUSE, Abelian varieties over finite fields (Ann. Sci. École Norm. Sup., n° 2, 1969, pp. 521-560). Zbl0188.53001MR42 #279
52. [Za] J. G. ZARHIN, Endomorphisms of abelian varieties over fields of finite characteristic (Math. USSR Izvest., Vol. 9, 1975, pp. 255-260). Zbl0345.14014MR51 #8114