Topics

No keywords indexed for this article. Browse by subject →

References
90
[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.
[3]
[Ar 2] S. J. Arakelov, Theory of intersections on an arithmetic surface, Proc. Int. Congr. of Mathematicians, 1, Vancouver, 1975, 405-408.
[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.
[5]
[Be 1] A. A. Beilinson, Higher regulators and values of L-functions, J. Soviet Math., 30 (1985), 2036-2070.
[6]
[Be 2] A. A. Beilinson, Height pairings between algebraic cycles, Contempory Math., 67 (1987), 1-24.
[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.
[8]
[Bl 2] S. Bloch, Algebraic K-theory and class-field theory for arithmetic surfaces, Ann. of Math., 114 (1981), 229-265.
[9]
[Bl 3] S. Bloch, Algebraic cycles and higher K-theory, Advances in Math., 61 (1986), 267-304.
[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.
[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.
[13]
[B-M] A. Borel and J. Moore, Homology theory for locally compact spaces, Michigan Math. J., 7 (1960), 137-159.
[14]
[C] J. Cheeger, Multiplication of differential characters, Instituto Nazionale di Alta Mathematica, Symposia Mathematica, XI (1973), 441-445.
[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.
[16]
[Co-G] M. Cornalba and P. Griffiths, Analytic Cycles and Vector Bundles on Non-compact Algebraic Varieties, Inv. Math., 28 (1975), 1-106.
[17]
[De 1] P. Deligne, Théorie de Hodge II, Pub. Math. I.H.E.S., 40 (1972), 5-57.
[18]
[De 2] P. Deligne, Le déterminant de la cohomologie, Contemporary Mathematics, 67 (1987), 93-178.
[19]
[Do] P. Dolbeault, Formes différentielles et cohomologie sur une variété analytique complexe I, Ann. of Math., 64 (1956), 83-130.
[20]
[E-S] S. Eilenberg and N. Steenrod, Foundations of algebraic topology, Princeton Univ. Press, 1952.
[21]
[F] G. Faltings, Calculus on arithmetic surfaces, Ann. of Math., 119 (1984), 387-424.
[22]
[Fu] W. Fulton, Intersection Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, Band 2, Berlin-Heidelberg, Springer Verlag, 1984.
[23]
[Gi 1] H. Gillet, Riemann-Roch Theorems for higher algebraic K-theory, Advances in Math., 40 (1981), 203-289.
[24]
[Gi 2] H. Gillet, Some new Gysin homomorphisms for the Chow homology of varieties, Proc. L.M.S. (3), 50 (1980), 57-68.
[25]
[Gi 3] H. Gillet, An introduction to higher dimensional Arakelov theory, Contemporary Math., 67 (1987), 209-228.
[26]
[Gi 4] H. Gillet, K-theory and intersection theory revisited, K-theory, 1 (1987), 407-415.
[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.
[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.
[29]
[G-S 3] H. Gillet and C. Soulé, Intersection theory using Adams operations, Inv. Math., 90 (1987), 243-278.
[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.
[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.
[32]
[Gr 1] D. Grayson, The K-theory of hereditary categories, J. Pure Appl. Algebra, 11 (1977), 67-74.
[33]
[Gr 2] D. Grayson, Localization for flat modules in algebraic K-theory, J. Algebra, 61 (1979), 463-496.
[34]
[G-H] P. Griffiths and J. Harris, Principles of algebraic geometry, John Wiley & Sons, 1978.
[35]
[G-H-V] W. Greub, S. Halperin and R. Vanstone, Connections, curvature and cohomology, 1, New York, Academic Press, 1972.
[36]
[Ha] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, 52, New York, Springer Verlag, 1977.
[37]
[H-L] M. Herera and D. Lieberman, Duality and the deRham cohomology of infinitesimal neighborhoods, Inv. Math., 13 (1971), 97-124.
[38]
[Hi] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math., 79 (1964), 109-326.
[39]
[Hr] P. Hriljac, Heights and Arakelov's Intersection Theory, Am. J. Math., 107 (1985), 23-38.
[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.
[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.
[42]
[K 1] J. King, The currents defined by algebraic varieties, Acta Math., 127 (1971), 185-220.
[43]
[K 2] J. King, Global residues and intersections on a complex manifold, Trans. Am. Math. Soc., 192 (1974), 163-199.
[44]
[K 3] J. King, Refined residues, Chern forms, and intersections, in Value distribution theory, Part A, New York, Dekker, 1974, 169-190.
[45]
[Kl] S. Kleiman, Motives, in Algebraic Geometry, Oslo, 1970 (F. OORT, ed.), Wolters-Noordhoff, Groningen, 1972, 53-82.
[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.
[47]
[L 1] S. Lang, Differential Manifolds, New York, Springer Verlag, 1985.
[48]
[L 2] S. Lang, Algebraic Number Theory, Addison-Wesley (Reading), 1970.
[49]
[Le] P. Lelong, Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France, 95 (1957), 239-262.
[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.

Showing 50 of 90 references

Metrics
125
Citations
90
References
Details
Published
Dec 07, 1990
Vol/Issue
72
Pages
93-174
License
View
Cite This Article
Henri Gillet, Christophe Soulé (1990). Arithmetic intersection theory. Publications Mathématiques de l'IHÉS, 72, 93-174. https://doi.org/10.1007/bf02699132
Related

You May Also Like

Théorie de Hodge : II

Pierre Deligne · 1971

963 citations

Groupes réductifs

Armand Borel, Jacques Tits · 1965

586 citations

Topological quantum field theory

Michael F. Atiyah · 1988

561 citations