Théorie de l'intersection et théorème de Riemann-Roch arithmétiques
Séminaire Bourbaki : volume 1990/91, exposés 730-744, Astérisque, no. 201-202-203 (1991), Talk no. 731, 46 p.
@incollection{SB_1990-1991__33__43_0,
     author = {Bost, Jean-Beno{\^\i}t},
     title = {Th\'eorie de l'intersection et th\'eor\`eme de {Riemann-Roch} arithm\'etiques},
     booktitle = {S\'eminaire Bourbaki : volume 1990/91, expos\'es 730-744},
     series = {Ast\'erisque},
     note = {talk:731},
     pages = {43--88},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {201-202-203},
     year = {1991},
     mrnumber = {1157838},
     zbl = {0780.14013},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1990-1991__33__43_0/}
}
TY  - CHAP
AU  - Bost, Jean-Benoît
TI  - Théorie de l'intersection et théorème de Riemann-Roch arithmétiques
BT  - Séminaire Bourbaki : volume 1990/91, exposés 730-744
AU  - Collectif
T3  - Astérisque
N1  - talk:731
PY  - 1991
SP  - 43
EP  - 88
IS  - 201-202-203
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/SB_1990-1991__33__43_0/
LA  - fr
ID  - SB_1990-1991__33__43_0
ER  - 
%0 Book Section
%A Bost, Jean-Benoît
%T Théorie de l'intersection et théorème de Riemann-Roch arithmétiques
%B Séminaire Bourbaki : volume 1990/91, exposés 730-744
%A Collectif
%S Astérisque
%Z talk:731
%D 1991
%P 43-88
%N 201-202-203
%I Société mathématique de France
%U http://www.numdam.org/item/SB_1990-1991__33__43_0/
%G fr
%F SB_1990-1991__33__43_0
Bost, Jean-Benoît. Théorie de l'intersection et théorème de Riemann-Roch arithmétiques, in Séminaire Bourbaki : volume 1990/91, exposés 730-744, Astérisque, no. 201-202-203 (1991), Talk no. 731, 46 p. http://www.numdam.org/item/SB_1990-1991__33__43_0/

[A1] S. J. Arakelov - Intersection theory for divisors on an arithmetic surface, Math. U.S.S.R. Izv. 8, 1974, 1167-1189. | MR | Zbl

[A2] S. J. Arakelov - Theory of intersection on an arithmetic surface, Proc. Int. Cong. of Math., Vancouver, vol. 1, 1978, 405-408. | MR | Zbl

[Be1] A. A. Beilinson - Higher regulators and values of L-functions, J. Soviet Math. 30,1985, 2036-2070. | MR | Zbl

[Be2] A. A. Beilinson - Height pairings between algebraic cycles, Contemp. Math. 67, 1-24. | MR | Zbl

[Bi1] J.-M. Bismut - Superconnections currents and complex immersions, Inventiones Math. 99, 1990, 59-113. | MR | Zbl

[Bi2] J.-M. Bismut - Koszul complexes, harmonic oscillators and the Todd class, Journal of the A.M.S. 3, 1990, 159-256. | MR | Zbl

[BGS1] J.-M. Bismut, H. Gillet et C. Soulé - Analytic torsion and holomorphic determinant bundles. I. Bott-Chern forms and analytic torsions ; II Direct images and Bott-Chern forms ; III Quillen metrics on holomorphic determinants, Commun. Math. Phys. 115, 1988, 49-78, 79-126, 301-351. | Zbl

[BGS2] J.-M. Bismut, H. Gillet et C. Soulé - Complex immersions and Arakelov geometry, Grothendieck Festschrift, Birkhäuser, 1990 | MR | Zbl

[BGS3] J.-M. Bismut, H. Gillet et C. Soulé - Bott-Chern currents and complex immersions, Duke Math. J. 60, 1990, 255-284. | MR | Zbl

[BL1] J.-M. Bismut et G. Lebeau - Immersions complexes et métriques de Quillen, Comptes rendus Acad. Sci. Paris 309, Série I, 1989, 487- 491. | MR | Zbl

[BL2] J.-M. Bismut et G. Lebeau - Complex immersions and Quillen metrics, Preprint, Orsay, 1990, 386 p. | MR

[BV] J.-M. Bismut et E. Vasserot - The asymptotic of the Ray-Singer analytic torsion associated with high powers of a positive line bundle, Commun. Math. Phys. 125, 1989, 355-367. | MR | Zbl

[B1] S. Bloch - Height pairings for algebraic cycles, Proc. Luminy conference on algebraic K-theory, J. Pure Appl. Algebra 34, 1984, 119-145. | MR | Zbl

[BC] R. Bott et S. S. Chern - Hermitian vector bundles and the equidis-

tribution of zeroes of their holomorphic sections, Acta Math. 114, 1968, 71-112.

[De] P. Deligne - Le déterminant de la cohomologie in Current trends in arithmetical algebraic geometry (K. Ribet ed.), Contemporary Math. 67, 1987, 93-177. | MR | Zbl

[Do] S. Donaldson - Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. 50, 1986, 1-26. | MR | Zbl

[E1] R. Elkik - Fibrés d'intersection et intégrales de classes de Chern, Ann. Sci. École Norm. Sup. 22, 4ème série, 1989, 195-226. | Numdam | MR | Zbl

[E2] R. Elkik - Métriques sur les fibrés d'intersection, Duke Math. J. 61, 1990, 303-328. | MR | Zbl

[Fa1] G. Faltings - Calculus on arithmetic surfaces, Annals of Math. 119, 1984, 387-424. | MR | Zbl

[Fa2] G. Faltings - Diophantine approximation on Abelian varieties, prepint, 1989.

[Fu] W. Fulton - Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, Band 2. Springer-Verlag, Berlin-Heidelberg-New York, 1984. | MR | Zbl

[G1] H. Gillet - Riemann-Roch theorems for higher algebraic K-theory, Adv. in Math. 40, 1981, 203-289. | MR | Zbl

[G2] H. Gillet - An introduction to higher dimensional Arakelov-theory, Contemporary Mathematics, 67, 209-228. | MR | Zbl

[GS1] H. Gillet et C. Soulé - Intersection sur les variétés d'Arakelov, Comptes rendus Acad. Sci. Paris, 299, Série I, 1984, 563-566. | MR | Zbl

[GS2] H. Gillet et C. Soulé - Classes caractéristiques sur les variétés d'Arakelov, Comptes rendus Acad. Sci. Paris, 301, Série I, 1985, 439-442. | MR | Zbl

[GS3] H. Gillet et C. Soulé - Direct images of Hermitian holomorphic bundles, Bull. A.M.S. 15, 1986, 209-212. | MR | Zbl

[GS4] H. Gillet et C. Soulé - Intersection theory using Adams operations, Inventiones Math. 90, 1987, 243-277. | MR | Zbl

[GS5] H. Gillet et C. Soulé - Arithmetic intersection theory, preprint I.H.E.S., 1988, à paraître aux Publications Mathématiques de l'I.H.E.S. | Numdam | MR | Zbl

[GS6] H. Gillet et C. Soulé - Characteristic classes for algebraic vector bundles with Hermitian metric, I, II, Annals of Math. 131, 1990, 163- 203. | MR | Zbl

[GS7] H. Gillet et C. Soulé - Analytic torsion and the arithmetic Todd germs, preprint I.H.E.S., 1988, à paraître dans Topology. | Zbl

[GS8] H. Gillet et C. Soulé - Differential characters and arithmetic intersection theory in "Algebraic K-theory : connections with geometry and topology", edited by J.F. Jardine and V.P. Snaith, NATO ASI Series C, Vol. 279, Kluwer Academic Publishers, 1989, 29-68. | MR | Zbl

[GS9] H. Gillet et C. Soulé - Amplitude arithmétique, Comptes Rendus Acad. Sci. Paris 307, 1988, 887-890. | MR | Zbl

[GS10] H. Gillet et C. Soulé - Un théorème de Riemann-Roch-Grothendieck arithmétique, Comptes Rendus Acad. Sci. Paris 309, Série I, 1989, 929-932. | MR | Zbl

[GH] P. Griffiths et J. Harris - Principles of algebraic geometry, John Wiley and Sons, 1978. | MR | Zbl

[KM] F. Knudsen et D. Mumford - The projectivity of the moduli space of stable curves, I, Preliminaries on "det" and "div", Math. Scand. 39, 1976, 19-55. | MR | Zbl

[La1] S. Lang - Fundamentals of diophantine geometry, Springer-Verlag, New York-Heidelberg-Berlin, 1983. | MR | Zbl

[La2] S. Lang - Introduction to Arakelov theory, Springer-Verlag, New York- Berlin-Heidelberg, 1988. | MR

[M] Yu. I. Manin - New dimensions in geometry in Arbeitstagung Bonn 1984, Ed. by F. Hirzebruch, J. Schwermer and S. Suter, Springer Lect. Notes in Math. n° 1111, 59-101. | MR | Zbl

[P] A. N. Parsin - Modular correspondences, heights and isogenies of Abelian varieties, Trudy Mat. Inst. Steklov 132, 1973 = Proc. Steklov Inst. Mat. 132, 1973, 243-270. | MR | Zbl

[Ph] P. Philippon - Sur des hauteurs alternatives, preprint, 1989.

[Q] D. Quillen - Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl. 14, 1985, 31-34. | Zbl

[RS] D. B. Ray et I. M. Singer - Analytic torsion for complex manifolds, Annals of Math. 98, 1973, 154-177. | MR | Zbl

[Se] J.-P. Serre - Algèbre locale, multiplicités, troisième édition, Lecture Notes in Math. 11, Springer-Verlag, Berlin, 1975. | MR | Zbl

[St] W. Stoll - About the value distribution of holomorphic maps into projective space, Acta Math. 123, 1969, 83-114. | MR | Zbl

[Sz] L. Szpiro - Séminaire sur les pinceaux arithmétiques : la conjecture de Mordell, Astérisque 127, 1985. | Numdam | MR | Zbl

[S1] C. Soulé - Opérations en K-théorie algébrique, Can. J. Math. 37, 1985, 488-550. | MR | Zbl

[S2] C. Soulé - Théorie de Nevanlinna et théorie d'Arakelov,Astérisque 183, 1990, 127-135. | Numdam | MR | Zbl

[S3] C. Soulé - Géométrie d'Arakelov et théorie des nombres transcendants, preprint I.H.E.S., 1989.

[V] P. Vojta - An extension of the Thue-Siegel-Dyson-Gel'fond theorem, preprint, 1989.

[W1] A. Weil - Sur l'analogie entre les corps de nombres algébriques et les corps de fonctions algébriques, Revue scientifique 77, 1939, 104-106. (= Œuvres scientifiques, Springer-Verlag, New York-Heidelberg-Berlin, volume I, 1980, [1939a], 236-240). | JFM

[W2] A. Weil - Une lettre et un extrait de lettre à Simone Weil, [1940a] in Œuvres scientifiques, Springer-Verlag, New York-Heidelberg-Berlin, volume I, 1980, 244-255.

[W3] A. Weil - Number theory and algebraic geometry, Proc. Intern. Math. Congress, Cambridge, Mass., vol. II, 90-10 (= Œuvres scientifiques, Springer-Verlag, New York-Heidelberg-Berlin, volume I, 1980, [1950b], 442-452). | Zbl

[W4] A. Weil - Elliptic functions according to Eisenstein and Kronecker, Ergebnisse der Mathematik und ihrer Grenzgebiete 88, Springer-Verlag, Berlin-Heidelberg-New York, 1976. | MR | Zbl

[Z] S. Zhang - Ample Hermitian line bundles on arithmetic surfaces, Preprint, october 1989 and may 1990.

[F3] G. Faltings - Lectures on the arithmetic Riemann-Roch theorem, notes by S. Zhang, preprint, 1991. | MR | Zbl

[GS11] H. Gillet et C. Soulé - An arithmetic Riemann-Roch theorem, preprint IHES, 1991. | MR