Arithmetic intersection theory

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1. [EGA IV] J. DIEUDONNÉ and A. GROTHENDIECK, Eléments de géométrie algébrique, Publ. Math. I.H.E.S., 20 (1964), 24 (1965), 28 (1966), 32 (1967). 
2. [Ar 1] S. J. ARAKELOV, Intersection theory of divisors on an arithmetic surface, Math. USSR Izvestija, 8 (1974), 1167-1180. Zbl0355.14002MR57 #12505
3. [Ar 2] S. J. ARAKELOV, Theory of intersections on an arithmetic surface, Proc. Int. Congr. of Mathematicians, 1, Vancouver, 1975, 405-408. Zbl0351.14003MR57 #6031
4. [B-F-M] P. BAUM, W. FULTON and R. MACPHERSON, Riemann-Roch for singular varieties, Publ. Math. I.H.E.S., 45 (1975), 101-145. Zbl0332.14003MR54 #317
5. [Be 1] A. A. BEILINSON, Higher regulators and values of L-functions, J. Soviet Math., 30 (1985), 2036-2070. Zbl0588.14013
6. [Be 2] A. A. BEILINSON, Height pairings between algebraic cycles, Contempory Math., 67 (1987), 1-24. Zbl0624.14005MR89g:11052
7. [Bl 1] S. BLOCH, Height pairings for algebraic cycles, in Proc. Luminy conference on algebraic K-theory (Luminy, 1983), J. Pure Appl. Algebra, 34 (1984), 119-145. Zbl0577.14004MR86h:14015
8. [Bl 2] S. BLOCH, Algebraic K-theory and class-field theory for arithmetic surfaces, Ann. of Math., 114 (1981), 229-265. Zbl0512.14009MR83m:14025
9. [Bl 3] S. BLOCH, Algebraic cycles and higher K-theory, Advances in Math., 61 (1986), 267-304. Zbl0608.14004MR88f:18010
10. [B-G-S] J. M. BISMUT, H. GILLET and C. SOULÉ, Complex immersions and Arakelov geometry, The Grothendieck Festschrift, 1, Progress in Mathematics, Birkhauser, Boston, 1990, 249-331. Zbl0744.14015MR92a:14019
11. [B-G] S. BLOCH and P. GRIFFITHS, A Theorem about normal functions associated to Lefschetz pencils on algebraic varieties, preprint, 1971. 
12. [B-H] A. BOREL and A. HAEFLIGER, La classe d'homologie fondamentale d'un espace analytique, Bull. Soc. Math. France, 89 (1961), 461-513. Zbl0102.38502MR26 #6990
13. [B-M] A. BOREL and J. MOORE, Homology theory for locally compact spaces, Michigan Math. J., 7 (1960), 137-159. Zbl0116.40301MR24 #A1123
14. [C] J. CHEEGER, Multiplication of differential characters, Instituto Nazionale di Alta Mathematica, Symposia Mathematica, XI (1973), 441-445. Zbl0285.53014MR58 #7648
15. [C-S] J. CHEEGER and J. SIMONS, Differential characters and geometric invariants, in Geometry and Topology, Lectures notes in Mathematics, 1167, Berlin, Springer Verlag, 1980, 50-80. Zbl0621.57010MR87g:53059
16. [Co-G] M. CORNALBA and P. GRIFFITHS, Analytic Cycles and Vector Bundles on Non-compact Algebraic Varieties, Inv. Math., 28 (1975), 1-106. Zbl0293.32026MR51 #3505
17. [De 1] P. DELIGNE, Théorie de Hodge II, Pub. Math. I.H.E.S., 40 (1972), 5-57. Zbl0219.14007
18. [De 2] P. DELIGNE, Le déterminant de la cohomologie, Contemporary Mathematics, 67 (1987), 93-178. Zbl0629.14008MR89b:32038
19. [Do] P. DOLBEAULT, Formes différentielles et cohomologie sur une variété analytique complexe I, Ann. of Math., 64 (1956), 83-130. Zbl0072.40603MR18,670e
20. [E-S] S. EILENBERG and N. STEENROD, Foundations of algebraic topology, Princeton Univ. Press, 1952. Zbl0047.41402MR14,398b
21. [F] G. FALTINGS, Calculus on arithmetic surfaces, Ann. of Math., 119 (1984), 387-424. Zbl0559.14005MR86e:14009
22. [Fu] W. FULTON, Intersection Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, Band 2, Berlin-Heidelberg, Springer Verlag, 1984. Zbl0541.14005MR85k:14004
23. [Gi 1] H. GILLET, Riemann-Roch Theorems for higher algebraic K-theory, Advances in Math., 40 (1981), 203-289. Zbl0478.14010MR83m:14013
24. [Gi 2] H. GILLET, Some new Gysin homomorphisms for the Chow homology of varieties, Proc. L.M.S. (3), 50 (1980), 57-68. Zbl0596.14003
25. [Gi 3] H. GILLET, An introduction to higher dimensional Arakelov theory, Contemporary Math., 67 (1987), 209-228. Zbl0621.14004MR88h:14005
26. [Gi 4] H. GILLET, K-theory and intersection theory revisited, K-theory, 1 (1987), 407-415. Zbl0651.14001MR89c:14014
27. [G-S 1] H. GILLET and C. SOULÉ, Intersection sur les variétés d'Arakelov, C.R. Acad. Sci. Paris, 299, Série I, 1984, 563-566. Zbl0607.14003MR86a:14019
28. [G-S 2] H. GILLET and C. SOULÉ, Classes caractéristiques en théorie d'Arakelov, C.R. Acad. Sci. Paris, 301, Série I, 1985, 439-442. Zbl0613.14007MR87f:14002
29. [G-S 3] H. GILLET and C. SOULÉ, Intersection theory using Adams operations, Inv. Math., 90 (1987), 243-278. Zbl0632.14009MR89d:14005
30. [G-S 4] H. GILLET and C. SOULÉ, Characteristic classes for algebraic vector bundles with Hermitian metrics, I, II, Ann. of Math., 131 (1990), 163-203 and 205-238. Zbl0715.14018MR91m:14032a
31. [G-S 5] H. GILLET and C. SOULÉ, Differential characters and arithmetic intersection theory, in Algebraic K-Theory: Connections with Geometry and Topology (ed. by J. F. JARDINE and V. P. SNAITH), NATO ASI, Series C, 279, Kluwer Academic Publishers, 1989, 29-68. Zbl0719.14003MR91j:14017
32. [Gr 1] D. GRAYSON, The K-theory of hereditary categories, J. Pure Appl. Algebra, 11 (1977), 67-74. Zbl0372.18004MR57 #16385
33. [Gr 2] D. GRAYSON, Localization for flat modules in algebraic K-theory, J. Algebra, 61 (1979), 463-496. Zbl0436.18010MR82c:14011
34. [G-H] P. GRIFFITHS and J. HARRIS, Principles of algebraic geometry, John Wiley & Sons, 1978. Zbl0408.14001MR80b:14001
35. [G-H-V] W. GREUB, S. HALPERIN and R. VANSTONE, Connections, curvature and cohomology, 1, New York, Academic Press, 1972. Zbl0322.58001
36. [Ha] R. HARTSHORNE, Algebraic Geometry, Graduate Texts in Mathematics, 52, New York, Springer Verlag, 1977. Zbl0367.14001MR57 #3116
37. [H-L] M. HERERA and D. LIEBERMAN, Duality and the deRham cohomology of infinitesimal neighborhoods, Inv. Math., 13 (1971), 97-124. Zbl0218.32005
38. [Hi] H. HIRONAKA, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math., 79 (1964), 109-326. Zbl0122.38603MR33 #7333
39. [Hr] P. HRILJAC, Heights and Arakelov's Intersection Theory, Am. J. Math., 107 (1985), 23-38. Zbl0593.14004MR86c:14024
40. [H-P] M. HARRIS and D. H. PHONG, Cohomologie de Dolbeault à croissance logarithmique à l'infini, C.R. Acad. Sci. Paris, 302 (1986), 307-310. Zbl0597.32025MR88a:32036
41. [J] J.-P. JOUANOLOU, Une suite exacte de Mayer-Vietoris en K-théorie algébrique, in Algebraic K-theory I, Proceedings of the 1972 Battelle Institute Conference, Lecture Notes in Mathematics, 341, Berlin, Springer Verlag, 1973, 293-316. Zbl0291.14006MR53 #13231
42. [K 1] J. KING, The currents defined by algebraic varieties, Acta Math., 127 (1971), 185-220. Zbl0224.32008MR52 #14359
43. [K 2] J. KING, Global residues and intersections on a complex manifold, Trans. Am. Math. Soc., 192 (1974), 163-199. Zbl0301.32005MR49 #3198
44. [K 3] J. KING, Refined residues, Chern forms, and intersections, in Value distribution theory, Part A, New York, Dekker, 1974, 169-190. Zbl0307.32002MR50 #7565
45. [Kl] S. KLEIMAN, Motives, in Algebraic Geometry, Oslo, 1970 (F. OORT, ed.), Wolters-Noordhoff, Groningen, 1972, 53-82. MR52 #3152
46. [K-M] F. KNUDSEN and D. MUMFORD, The projectivity of the moduli space of stable curves I, preliminaries on “det” and “Div”, Math. Scand., 39 (1976), 19-55. Zbl0343.14008MR55 #10465
47. [L 1] S. LANG, Differential Manifolds, New York, Springer Verlag, 1985. Zbl0551.58001MR85m:58001
48. [L 2] S. LANG, Algebraic Number Theory, Addison-Wesley (Reading), 1970. Zbl0211.38404MR44 #181
49. [Le] P. LELONG, Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France, 95 (1957), 239-262. Zbl0079.30901MR20 #2465
50. [Q] D. QUILLEN, Higher Algebraic K-theory I, in Algebraic K-theory I, Lecture Notes in Mathematics, 341, Berlin, Springer Verlag, 1973, 85-147. Zbl0292.18004MR49 #2895
51. [deRh] G. DERHAM, Variétés différentiables : formes, courants, formes harmoniques, Paris, Hermann, 1960. Zbl0089.08105
52. [R] J. ROBERTS, Chow's moving lemma, in Algebraic Geometry, Oslo, 1970 (F. OORT ed.), Wolters-Noordhoff, Groningen, 1972, 89-96. MR52 #3154
53. [Sch] L. SCHWARTZ, Théorie des distributions, nouvelle édition, Paris, Hermann, 1966. Zbl0149.09501MR35 #730
54. [Se] J.-P. SERRE, Algèbre locale, Multiplicités, 3rd ed., Lecture Notes in Mathematics, 11, Berlin, Springer Verlag, 1975. Zbl0296.13018
55. [Sha] B. V. SHABAT, Distribution of values of holomorphic mappings, Translations of Mathematical Monographs, 61, Am. Math. Soc. (Providence), 1985. Zbl0564.32016MR86k:32023
56. [She] V. V. SHECHTMANN, Riemann-Roch's theorem in Algebraic K-theory, Dep. Viniti, No. 2425-79 (1979). 
57. [So] C. SOULÉ, Opérations en K-théorie algébrique, Canadian Journal of Math., 37 (1985), 488-550. Zbl0575.14015MR87b:18013
58. [Sp] E. SPANIER, Algebraic Topology, New York, McGraw-Hill, 1966. Zbl0145.43303MR35 #1007
59. [Sz 1] L. SZPIRO, Séminaire sur les pinceaux de courbes de genre au moins deux, Astérisque, n° 86 (1981), Société Math. de France. Zbl0463.00009MR83c:14020
60. [Sz 2] L. SZPIRO, Présentation de la théorie d'Arakelov, Contemporary Math., 67 (1987), 279-293. Zbl0634.14012MR89c:14005
61. [V] J.-L. VERDIER, Le théorème de Riemann-Roch pour les intersections complètes, Astérisque, n° 36-37 (1976), 189-228. Zbl0334.14026
62. [W] C. WEIBEL, Homotopy algebraic K-theory, Contemporary Mathematics, 83 (1989), 461-488. Zbl0669.18007MR90d:18006
63. [We 1] A. WEIL, Sur l'analogie entre les corps de nombres algébriques et les corps de fonctions algébriques, in Collected Papers, 1, New York, Springer Verlag, 1980, 236-240. 
64. [We 2] A. WEIL, Letter to Simone Weil [1940a], in Collected Papers, 1, New York, Springer Verlag, 1980, 244-255. 
65. [We l] R. O. WELLS, Differential analysis on complex manifolds, Englewood Cliffs, N.J., Prentice Hall, 1973. Zbl0262.32005MR58 #24309a
66. [J] J.-P. JOUANOLOU, Une suite exacte de Mayer-Vietoris en K-théorie algébrique, in Algebraic K-theory I, Proceedings of the 1972 Battelle Institute Conference, Lecture Notes in Mathematics, 341, Berlin, Springer Verlag, 1973, 293-316. Zbl0291.14006MR53 #13231
67. [K 1] J. KING, The currents defined by algebraic varieties, Acta Math., 127 (1971), 185-220. Zbl0224.32008MR52 #14359
68. [K 2] J. KING, Global residues and intersections on a complex manifold, Trans. Am. Math. Soc., 192 (1974), 163-199. Zbl0301.32005MR49 #3198
69. [K 3] J. KING, Refined residues, Chern forms, and intersections, in Value distribution theory, Part A, New York, Dekker, 1974, 169-190. Zbl0307.32002MR50 #7565
70. [Kl] S. KLEIMAN, Motives, in Algebraic Geometry, Oslo, 1970 (F. OORT, ed.), Wolters-Noordhoff, Groningen, 1972, 53-82. Zbl0285.14005MR52 #3152
71. [K-M] F. KNUDSEN and D. MUMFORD, The projectivity of the moduli space of stable curves I, preliminaries on “det” and “Div”, Math. Scand., 39 (1976), 19-55. Zbl0343.14008MR55 #10465
72. [L 1] S. LANG, Differential Manifolds, New York, Springer Verlag, 1985. Zbl0551.58001MR85m:58001
73. [L 2] S. LANG, Algebraic Number Theory, Addison-Wesley (Reading), 1970. Zbl0211.38404MR44 #181
74. [Le] P. LELONG, Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France, 95 (1957), 239-262. Zbl0079.30901MR20 #2465
75. [Q] D. QUILLEN, Higher Algebraic K-theory I, in Algebraic K-theory I, Lecture Notes in Mathematics, 341, Berlin, Springer Verlag, 1973, 85-147. Zbl0292.18004MR49 #2895
76. [deRh] G. DERHAM, Variétés différentiables : formes, courants, formes harmoniques, Paris, Hermann, 1960. Zbl0089.08105
77. [R] J. ROBERTS, Chow's moving lemma, in Algebraic Geometry, Oslo, 1970 (F. OORT ed.), Wolters-Noordhoff, Groningen, 1972, 89-96. MR52 #3154
78. [Sch] L. SCHWARTZ, Théorie des distributions, nouvelle édition, Paris, Hermann, 1966. Zbl0149.09501MR35 #730
79. [Se] J.-P. SERRE, Algèbre locale, Multiplicités, 3rd ed., Lecture Notes in Mathematics, 11, Berlin, Springer Verlag, 1975. Zbl0296.13018
80. [Sha] B. V. SHABAT, Distribution of values of holomorphic mappings, Translations of Mathematical Monographs, 61, Am. Math. Soc. (Providence), 1985. Zbl0564.32016MR86k:32023
81. [She] V. V. SHECHTMANN, Riemann-Roch's theorem in Algebraic K-theory, Dep. Viniti, No. 2425-79 (1979). 
82. [So] C. SOULÉ, Opérations en K-théorie algébrique, Canadian Journal of Math., 37 (1985), 488-550. Zbl0575.14015MR87b:18013
83. [Sp] E. SPANIER, Algebraic Topology, New York, McGraw-Hill, 1966. Zbl0145.43303MR35 #1007
84. [Sz 1] L. SZPIRO, Séminaire sur les pinceaux de courbes de genre au moins deux, Astérisque, n° 86 (1981), Société Math. de France. Zbl0463.00009MR83c:14020
85. [Sz 2] L. SZPIRO, Présentation de la théorie d'Arakelov, Contemporary Math., 67 (1987), 279-293. Zbl0634.14012MR89c:14005
86. [V] J.-L. VERDIER, Le théorème de Riemann-Roch pour les intersections complètes, Astérisque, n° 36-37 (1976), 189-228. Zbl0334.14026
87. [W] C. WEIBEL, Homotopy algebraic K-theory, Contemporary Mathematics, 83 (1989), 461-488. Zbl0669.18007MR90d:18006
88. [We 1] A. WEIL, Sur l'analogie entre les corps de nombres algébriques et les corps de fonctions algébriques, in Collected Papers, 1, New York, Springer Verlag, 1980, 236-240. 
89. [We 2] A. WEIL, Letter to Simone Weil [1940a], in Collected Papers, 1, New York, Springer Verlag, 1980, 244-255. 
90. [Wel] R. O. WELLS, Differential analysis on complex manifolds, Englewood Cliffs, N.J., Prentice Hall, 1973. Zbl0262.32005MR58 #24309a

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