On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field
Schoen, Chad
Annales scientifiques de l'École Normale Supérieure, Tome 28 (1995), p. 1-50 / Harvested from Numdam
@article{ASENS_1995_4_28_1_1_0,
     author = {Schoen, Chad},
     title = {On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {28},
     year = {1995},
     pages = {1-50},
     doi = {10.24033/asens.1708},
     mrnumber = {95j:14010},
     zbl = {0839.14004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1995_4_28_1_1_0}
}
Schoen, Chad. On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field. Annales scientifiques de l'École Normale Supérieure, Tome 28 (1995) pp. 1-50. doi : 10.24033/asens.1708. http://gdmltest.u-ga.fr/item/ASENS_1995_4_28_1_1_0/

[A1] J. Alperin, Local Representation Theory (Cambridge studies in advanced math., Vol. 11, Cambridge University press, Cambridge, 1986). | MR 860771 | MR 87i:20002 | Zbl 0593.20003

[A-M] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading Mass., 1969. | MR 242802 | MR 39 #4129 | Zbl 0175.03601

[B] S. Bloch, Algebraic cycles and values of L-functions (J. reine und angew. Math., Vol. 350, 1984, pp. 94-108). | MR 743535 | MR 85i:11052 | Zbl 0527.14008

[B1] S. Bloch, Torsion algebraic cycles and a theorem of Roitman (Compositio Math. Vol. 39, 1979, pp. 107-127). | Numdam | MR 539002 | MR 80k:14012 | Zbl 0463.14002

[B2] S. Bloch, Algebraic cycles and values of L-functions II (Duke Math. J., Vol. 52, 1985, pp. 379-397). | MR 792179 | MR 87a:14021 | Zbl 0628.14006

[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). | Zbl 0502.14009

[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). | MR 664643 | MR 83h:14008 | Zbl 0504.14016

[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). | MR 855873 | Zbl 0603.14011

[Bi-Ku] B. Birch and Kuyk, ed., Modular functions of one variable IV (Lect. Notes Math., n° 476, 1972). | MR 376533 | MR 51 #12708 | Zbl 0315.14014

[Co-Ra] J.-L. Colliot-Thélène and W. Raskind, K2-cohomology and the second Chow group (Math. Ann. n° 270, 1985, pp. 165-199). | MR 86m:14005 | Zbl 0536.14004

[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). | MR 85d:14010 | Zbl 0574.14004

[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). | Numdam | Zbl 0206.49901

[D2] P. Deligne, Variétés abéliennes ordinaires sur un corps fini (Inv. math., Vol. 8, 1969, pp. 238-243). | MR 40 #7270 | Zbl 0179.26201

[Fu] W. Fulton, Intersection Theory (Ergeb. Math. Grenzgeb., Vol. 2, Springer-Verlag, 1984). | MR 85k:14004 | Zbl 0541.14005

[Gro] B. Gross, Representation theory and the cuspidal group of X (p) (Duke Math. J., Vol. 54, 1987, pp. 67-75). | MR 89b:11052 | Zbl 0629.14021

[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). | MR 57 #3132 | Zbl 0349.14012

[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). | Numdam | Zbl 0238.14014

[Ha] B. Harris, Homological versus algebraic equivalence in a Jacobian (Proc. Nat. Acad. Sci. U.S.A., Vol. 80, 1983, pp. 1157-1158). | MR 84m:14009 | Zbl 0523.14006

[Ja] U. Jannsen, Mixed motives and algebraic K-theory (Lect. Notes Math., Vol. 1400, Berlin Heidelberg New York, Springer, 1990). | MR 91g:14008 | Zbl 0691.14001

[La1] S. Lang, Sur les séries L d'une variété algébrique (Bull. Soc. Math. France, Vol. 84, 1956, pp. 385-407). | Numdam | MR 19,578c | Zbl 0089.26301

[La2] S. Lang, Elliptic Functions, Addison-Wesley, London, 1973. | MR 53 #13117 | Zbl 0316.14001

[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). | MR 56 #3017 | Zbl 0341.14006

[Lig] G. Ligozat, Courbes Modulaires de Genre 1 (Bull. Soc. Math. France, Vol. 43, Paris, 1975). | Numdam | MR 54 #5121 | Zbl 0322.14011

[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). | Zbl 0525.18008

[Mi] J. Milne, Etale Cohomology, Princeton University Press, Princeton, 1980. | MR 81j:14002 | Zbl 0433.14012

[Mi2] J. Milne, Zero cycles on algebraic varieties in non-zero characteristic : Rojtman's theorem (Compositio Math., Vol. 47, 1982, pp. 271-287). | Numdam | MR 85b:14011 | Zbl 0506.14006

[Mi3] J. Milne, Arithmetic Duality Theorems, Academic Press, Orlando, 1986. | MR 88e:14028 | Zbl 0613.14019

[Mu] D. Mumford, Abelian Varieties, Oxford University Press, Oxford, 1970. | MR 44 #219 | Zbl 0223.14022

[Ne] J. Nekovář, Kolyvagin's method for Chow groups of Kuga-Sato varieties (Inv. Math., Vol. 107, 1992, pp. 99-125). | MR 93b:11076 | Zbl 0729.14004

[Ogg] A. Ogg, Elliptic curves and wild ramification (Amer. J. Math., Vol. 89, 1967, pp. 1-21). | MR 34 #7509 | Zbl 0147.39803

[Ra] W. Raskind, W., A finiteness theorem in the Galois Cohomology of algebraic number fields (Trans. AMS, Vol. 303, 1987, pp. 743-749). | MR 88m:11098 | Zbl 0648.12009

[Ro] J. Roberts, Chow's moving lemma, in Algebraic Geometry, F. Oort ed., Wolters-Noordhoff Publ. Groningen, 1972, pp. 89-96. | MR 52 #3154

[Roi] A. A. Roitman, The torsion of the group of 0-cycles modulo rational equivalence (Ann. of Math., Vol. 111, 1980, pp. 553-569). | MR 81g:14003 | Zbl 0504.14006

[Sch-BB] C. Schoen, Complex multiplication cycles and the conjecture of Beilinson and Bloch (Trans. A.M.S., Vol. 339, 1993, pp. 87-115). | MR 93k:14011 | Zbl 0811.14003

[Sch-CM] C. Schoen, Complex multiplication cycles on elliptic modular threefolds (Duke Math J., Vol. 53, 1986, pp. 771-794). | MR 87m:14041 | Zbl 0623.14018

[Sch-FP] C. Schoen, On fiber products of rational elliptic surfaces with section (Math. Z., Vol. 197, 1988, pp. 177-199). | MR 89c:14062 | Zbl 0631.14032

[Sch-MR] C. Schoen, On certain modular representations in the cohomology of algebraic curves (J. of Algebra, Vol. 135, 1990, pp. 1-18). | MR 91h:14021 | Zbl 0727.20033

[Sch-T] C. Schoen, Some examples of torsion in the Griffiths group (Math. Ann., Vol. 293, 1992, pp. 651-679). | MR 94d:14009 | Zbl 0790.14006

[Se1] J. P. Serre, Linear representations of finite groups (Graduate Texts in Math., Vol. 42, Springer-Verlag, New York, 1977). | MR 56 #8675 | Zbl 0355.20006

[Se2] J. P. Serre, Local Fields (Graduate Texts in Math., Vol. 67, Springer-Verlag, New York, 1979). | MR 82e:12016 | Zbl 0423.12016

[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). | MR 45 #5111 | Zbl 0225.14015

[Sh2] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press, 1971. | Zbl 0221.10029

[Si1] J. Silverman, The Arithmetic of elliptic curves, Springer Verlag, 1986. | MR 87g:11070 | Zbl 0585.14026

[So] C. Soulé, Groupes de Chow et K-théorie de variétés sur un corps fini (Math. Ann., Vol. 268, 1984, pp. 317-345). | MR 86k:14017 | Zbl 0573.14001

[St] J. Steenbrink, Limits of Hodge structures (Invent. Math. Vol. 31, 1976, pp. 229-257). | MR 55 #2894 | Zbl 0303.14002

[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). | MR 37 #5225 | Zbl 0221.10023

[Su] N. Suwa, Sur l'image de l'application d'Abel-Jacobi de Bloch (Bull. Soc. math. France, Vol. 116, 1988, pp. 69-101). | Numdam | MR 89j:14003 | Zbl 0686.14006

[Ta1] J. Tate, Relations between K2 and Galois cohomology (Invent. Math., Vol. 36, 1976, pp. 257-274). | MR 55 #2847 | Zbl 0359.12011

[Ta2] J. Tate, Classes d'isogénie des variétés abéliennes sur un corps fini (d'après Honda) (Sém. Bourbaki, n° 352, 1968). | Numdam | Zbl 0212.25702

[Ta3] J. Tate, Endomorphisms of Abelian Varieties (Inv. Math., Vol. 2, 1966, pp. 134-144). | MR 34 #5829 | Zbl 0147.20303

[Wa] W. Waterhouse, Abelian varieties over finite fields (Ann. Sci. École Norm. Sup., n° 2, 1969, pp. 521-560). | Numdam | MR 42 #279 | Zbl 0188.53001

[Za] J. G. Zarhin, Endomorphisms of abelian varieties over fields of finite characteristic (Math. USSR Izvest., Vol. 9, 1975, pp. 255-260). | MR 51 #8114 | Zbl 0345.14014