@article{PMIHES_1990__72__93_0, author = {Gillet, Henri and Soul\'e, Christophe}, title = {Arithmetic intersection theory}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {93--174}, publisher = {Institut des Hautes \'Etudes Scientifiques}, volume = {72}, year = {1990}, mrnumber = {1087394}, zbl = {0741.14012}, language = {en}, url = {http://archive.numdam.org/item/PMIHES_1990__72__93_0/} }
TY - JOUR AU - Gillet, Henri AU - Soulé, Christophe TI - Arithmetic intersection theory JO - Publications Mathématiques de l'IHÉS PY - 1990 SP - 93 EP - 174 VL - 72 PB - Institut des Hautes Études Scientifiques UR - http://archive.numdam.org/item/PMIHES_1990__72__93_0/ LA - en ID - PMIHES_1990__72__93_0 ER -
Gillet, Henri; Soulé, Christophe. Arithmetic intersection theory. Publications Mathématiques de l'IHÉS, Volume 72 (1990), pp. 93-174. http://archive.numdam.org/item/PMIHES_1990__72__93_0/
[EGA IV] Eléments de géométrie algébrique, Publ. Math. I.H.E.S., 20 (1964), 24 (1965), 28 (1966), 32 (1967). | Numdam
and ,[Ar 1] Intersection theory of divisors on an arithmetic surface, Math. USSR Izvestija, 8 (1974), 1167-1180. | MR | Zbl
,[Ar 2] Theory of intersections on an arithmetic surface, Proc. Int. Congr. of Mathematicians, 1, Vancouver, 1975, 405-408. | MR | Zbl
,[B-F-M] Riemann-Roch for singular varieties, Publ. Math. I.H.E.S., 45 (1975), 101-145. | Numdam | MR | Zbl
, and ,[Be 1] Higher regulators and values of L-functions, J. Soviet Math., 30 (1985), 2036-2070. | Zbl
,[Be 2] Height pairings between algebraic cycles, Contempory Math., 67 (1987), 1-24. | MR | Zbl
,[Bl 1] Height pairings for algebraic cycles, in Proc. Luminy conference on algebraic K-theory (Luminy, 1983), J. Pure Appl. Algebra, 34 (1984), 119-145. | MR | Zbl
,[Bl 2] Algebraic K-theory and class-field theory for arithmetic surfaces, Ann. of Math., 114 (1981), 229-265. | MR | Zbl
,[Bl 3] Algebraic cycles and higher K-theory, Advances in Math., 61 (1986), 267-304. | MR | Zbl
,[B-G-S] Complex immersions and Arakelov geometry, The Grothendieck Festschrift, 1, Progress in Mathematics, Birkhauser, Boston, 1990, 249-331. | MR | Zbl
, and ,[B-G] A Theorem about normal functions associated to Lefschetz pencils on algebraic varieties, preprint, 1971.
and ,[B-H] La classe d'homologie fondamentale d'un espace analytique, Bull. Soc. Math. France, 89 (1961), 461-513. | EuDML | Numdam | MR | Zbl
and ,[B-M] Homology theory for locally compact spaces, Michigan Math. J., 7 (1960), 137-159. | MR | Zbl
and ,[C] Multiplication of differential characters, Instituto Nazionale di Alta Mathematica, Symposia Mathematica, XI (1973), 441-445. | MR | Zbl
,[C-S] Differential characters and geometric invariants, in Geometry and Topology, Lectures notes in Mathematics, 1167, Berlin, Springer Verlag, 1980, 50-80. | MR | Zbl
and ,[Co-G] Analytic Cycles and Vector Bundles on Non-compact Algebraic Varieties, Inv. Math., 28 (1975), 1-106. | EuDML | MR | Zbl
and ,[De 1] Théorie de Hodge II, Pub. Math. I.H.E.S., 40 (1972), 5-57. | EuDML | Numdam | Zbl
,[De 2] Le déterminant de la cohomologie, Contemporary Mathematics, 67 (1987), 93-178. | MR | Zbl
,[Do] Formes différentielles et cohomologie sur une variété analytique complexe I, Ann. of Math., 64 (1956), 83-130. | MR | Zbl
,[E-S] Foundations of algebraic topology, Princeton Univ. Press, 1952. | MR | Zbl
and ,[F] Calculus on arithmetic surfaces, Ann. of Math., 119 (1984), 387-424. | MR | Zbl
,[Fu] Intersection Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, Band 2, Berlin-Heidelberg, Springer Verlag, 1984. | MR | Zbl
,[Gi 1] Riemann-Roch Theorems for higher algebraic K-theory, Advances in Math., 40 (1981), 203-289. | MR | Zbl
,[Gi 2] Some new Gysin homomorphisms for the Chow homology of varieties, Proc. L.M.S. (3), 50 (1980), 57-68. | Zbl
,[Gi 3] An introduction to higher dimensional Arakelov theory, Contemporary Math., 67 (1987), 209-228. | MR | Zbl
,[Gi 4] K-theory and intersection theory revisited, K-theory, 1 (1987), 407-415. | MR | Zbl
,[G-S 1] Intersection sur les variétés d'Arakelov, C.R. Acad. Sci. Paris, 299, Série I, 1984, 563-566. | MR | Zbl
and ,[G-S 2] Classes caractéristiques en théorie d'Arakelov, C.R. Acad. Sci. Paris, 301, Série I, 1985, 439-442. | MR | Zbl
and ,[G-S 3] Intersection theory using Adams operations, Inv. Math., 90 (1987), 243-278. | EuDML | MR | Zbl
and ,[G-S 4] Characteristic classes for algebraic vector bundles with Hermitian metrics, I, II, Ann. of Math., 131 (1990), 163-203 and 205-238. | MR | Zbl
and ,[G-S 5] 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. | MR | Zbl
and ,[Gr 1] The K-theory of hereditary categories, J. Pure Appl. Algebra, 11 (1977), 67-74. | MR | Zbl
,[Gr 2] Localization for flat modules in algebraic K-theory, J. Algebra, 61 (1979), 463-496. | MR | Zbl
,[G-H] Principles of algebraic geometry, John Wiley & Sons, 1978. | MR | Zbl
and ,[G-H-V] Connections, curvature and cohomology, 1, New York, Academic Press, 1972. | Zbl
, and ,[Ha] Algebraic Geometry, Graduate Texts in Mathematics, 52, New York, Springer Verlag, 1977. | MR | Zbl
,[H-L] Duality and the deRham cohomology of infinitesimal neighborhoods, Inv. Math., 13 (1971), 97-124. | EuDML | Zbl
and ,[Hi] Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math., 79 (1964), 109-326. | MR | Zbl
,[Hr] Heights and Arakelov's Intersection Theory, Am. J. Math., 107 (1985), 23-38. | MR | Zbl
,[H-P] Cohomologie de Dolbeault à croissance logarithmique à l'infini, C.R. Acad. Sci. Paris, 302 (1986), 307-310. | MR | Zbl
and ,[J] 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. | MR | Zbl
,[K 1] The currents defined by algebraic varieties, Acta Math., 127 (1971), 185-220. | MR | Zbl
,[K 2] Global residues and intersections on a complex manifold, Trans. Am. Math. Soc., 192 (1974), 163-199. | MR | Zbl
,[K 3] Refined residues, Chern forms, and intersections, in Value distribution theory, Part A, New York, Dekker, 1974, 169-190. | MR | Zbl
,[Kl] Motives, in Algebraic Geometry, Oslo, 1970 (F. OORT, ed.), Wolters-Noordhoff, Groningen, 1972, 53-82. | MR | Zbl
,[K-M] The projectivity of the moduli space of stable curves I, preliminaries on “det” and “Div”, Math. Scand., 39 (1976), 19-55. | EuDML | MR | Zbl
and ,[L 1] Differential Manifolds, New York, Springer Verlag, 1985. | MR | Zbl
,[L 2] Algebraic Number Theory, Addison-Wesley (Reading), 1970. | MR | Zbl
,[Le] Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France, 95 (1957), 239-262. | EuDML | Numdam | MR | Zbl
,[Q] Higher Algebraic K-theory I, in Algebraic K-theory I, Lecture Notes in Mathematics, 341, Berlin, Springer Verlag, 1973, 85-147. | MR | Zbl
,[deRh] Variétés différentiables : formes, courants, formes harmoniques, Paris, Hermann, 1960. | Zbl
,[R] Chow's moving lemma, in Algebraic Geometry, Oslo, 1970 (F. OORT ed.), Wolters-Noordhoff, Groningen, 1972, 89-96. | MR
,[Sch] Théorie des distributions, nouvelle édition, Paris, Hermann, 1966. | MR | Zbl
,[Se] Algèbre locale, Multiplicités, 3rd ed., Lecture Notes in Mathematics, 11, Berlin, Springer Verlag, 1975. | Zbl
,[Sha] Distribution of values of holomorphic mappings, Translations of Mathematical Monographs, 61, Am. Math. Soc. (Providence), 1985. | MR | Zbl
,[She] Riemann-Roch's theorem in Algebraic K-theory, Dep. Viniti, No. 2425-79 (1979).
,[So] Opérations en K-théorie algébrique, Canadian Journal of Math., 37 (1985), 488-550. | MR | Zbl
,[Sp] Algebraic Topology, New York, McGraw-Hill, 1966. | MR | Zbl
,[Sz 1] Séminaire sur les pinceaux de courbes de genre au moins deux, Astérisque, n° 86 (1981), Société Math. de France. | Numdam | MR | Zbl
,[Sz 2] Présentation de la théorie d'Arakelov, Contemporary Math., 67 (1987), 279-293. | MR | Zbl
,[V] Le théorème de Riemann-Roch pour les intersections complètes, Astérisque, n° 36-37 (1976), 189-228. | Numdam | Zbl
,[W] Homotopy algebraic K-theory, Contemporary Mathematics, 83 (1989), 461-488. | MR | Zbl
,[We 1] 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.
,[We 2] Letter to Simone Weil [1940a], in Collected Papers, 1, New York, Springer Verlag, 1980, 244-255.
,[We l] Differential analysis on complex manifolds, Englewood Cliffs, N.J., Prentice Hall, 1973. | MR | Zbl
,[J] 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. | MR | Zbl
,[K 1] The currents defined by algebraic varieties, Acta Math., 127 (1971), 185-220. | MR | Zbl
,[K 2] Global residues and intersections on a complex manifold, Trans. Am. Math. Soc., 192 (1974), 163-199. | MR | Zbl
,[K 3] Refined residues, Chern forms, and intersections, in Value distribution theory, Part A, New York, Dekker, 1974, 169-190. | MR | Zbl
,[Kl] Motives, in Algebraic Geometry, Oslo, 1970 (F. OORT, ed.), Wolters-Noordhoff, Groningen, 1972, 53-82. | MR | Zbl
,[K-M] The projectivity of the moduli space of stable curves I, preliminaries on “det” and “Div”, Math. Scand., 39 (1976), 19-55. | EuDML | MR | Zbl
and ,[L 1] Differential Manifolds, New York, Springer Verlag, 1985. | MR | Zbl
,[L 2] Algebraic Number Theory, Addison-Wesley (Reading), 1970. | MR | Zbl
,[Le] Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France, 95 (1957), 239-262. | EuDML | Numdam | MR | Zbl
,[Q] Higher Algebraic K-theory I, in Algebraic K-theory I, Lecture Notes in Mathematics, 341, Berlin, Springer Verlag, 1973, 85-147. | MR | Zbl
,[deRh] Variétés différentiables : formes, courants, formes harmoniques, Paris, Hermann, 1960. | Zbl
,[R] Chow's moving lemma, in Algebraic Geometry, Oslo, 1970 (F. OORT ed.), Wolters-Noordhoff, Groningen, 1972, 89-96. | MR | Zbl
,[Sch] Théorie des distributions, nouvelle édition, Paris, Hermann, 1966. | MR | Zbl
,[Se] Algèbre locale, Multiplicités, 3rd ed., Lecture Notes in Mathematics, 11, Berlin, Springer Verlag, 1975. | Zbl
,[Sha] Distribution of values of holomorphic mappings, Translations of Mathematical Monographs, 61, Am. Math. Soc. (Providence), 1985. | MR | Zbl
,[She] Riemann-Roch's theorem in Algebraic K-theory, Dep. Viniti, No. 2425-79 (1979).
,[So] Opérations en K-théorie algébrique, Canadian Journal of Math., 37 (1985), 488-550. | MR | Zbl
,[Sp] Algebraic Topology, New York, McGraw-Hill, 1966. | MR | Zbl
,[Sz 1] Séminaire sur les pinceaux de courbes de genre au moins deux, Astérisque, n° 86 (1981), Société Math. de France. | Numdam | MR | Zbl
,[Sz 2] Présentation de la théorie d'Arakelov, Contemporary Math., 67 (1987), 279-293. | MR | Zbl
,[V] Le théorème de Riemann-Roch pour les intersections complètes, Astérisque, n° 36-37 (1976), 189-228. | Numdam | Zbl
,[W] Homotopy algebraic K-theory, Contemporary Mathematics, 83 (1989), 461-488. | MR | Zbl
,[We 1] 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.
,[We 2] Letter to Simone Weil [1940a], in Collected Papers, 1, New York, Springer Verlag, 1980, 244-255.
,[Wel] Differential analysis on complex manifolds, Englewood Cliffs, N.J., Prentice Hall, 1973. | MR | Zbl
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