Hermitian vector bundles and extension groups on arithmetic schemes II. The arithmetic Atiyah extension

Bost, Jean-Benoît ; Künnemann, Klaus

From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 361-424.

MR Zbl

@incollection{AST_2009__327__361_0,
     author = {Bost, Jean-Beno{\^\i}t and K\"unnemann, Klaus},
     title = {Hermitian vector bundles and extension groups on arithmetic schemes {II.} {The} arithmetic {Atiyah} extension},
     booktitle = {From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut},
     editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping},
     series = {Ast\'erisque},
     pages = {361--424},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {327},
     year = {2009},
     mrnumber = {2642363},
     zbl = {1200.14049},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2009__327__361_0/}
}

TY  - CHAP
AU  - Bost, Jean-Benoît
AU  - Künnemann, Klaus
TI  - Hermitian vector bundles and extension groups on arithmetic schemes II. The arithmetic Atiyah extension
BT  - From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut
AU  - Collectif
ED  - Dai Xianzhe
ED  - Léandre Rémi
ED  - Xiaonan Ma
ED  - Zhang Weiping
T3  - Astérisque
PY  - 2009
SP  - 361
EP  - 424
IS  - 327
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2009__327__361_0/
LA  - en
ID  - AST_2009__327__361_0
ER  -

%0 Book Section
%A Bost, Jean-Benoît
%A Künnemann, Klaus
%T Hermitian vector bundles and extension groups on arithmetic schemes II. The arithmetic Atiyah extension
%B From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut
%A Collectif
%E Dai Xianzhe
%E Léandre Rémi
%E Xiaonan Ma
%E Zhang Weiping
%S Astérisque
%D 2009
%P 361-424
%N 327
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_2009__327__361_0/
%G en
%F AST_2009__327__361_0

Bost, Jean-Benoît; Künnemann, Klaus. Hermitian vector bundles and extension groups on arithmetic schemes II. The arithmetic Atiyah extension, dans From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 361-424. http://archive.numdam.org/item/AST_2009__327__361_0/

Bibliographie
Cité par

[1] B. Angéniol & M. Lejeune-Jalabert - Calcul différentiel et classes caractéristiques en géométrie algébrique, Travaux en Cours, vol. 38, Hermann, 1989. | MR | Zbl

[2] M. F. Atiyah - "Complex analytic connections in fibre bundles", Trans. Amer. Math. Soc. 85 (1957), p. 181-207. | DOI | MR | Zbl

[3] A. Baker & G. Wüstholz - "Logarithmic forms and Diophantine geometry", New Mathematical Monographs, Cambridge Univ. Press, 2007. | MR | Zbl

[4] D. Bertrand - "Points rationnels sur les sous-groupes compacts des groupes algébriques", Experiment. Math. 4 (1995), p. 145-151. | DOI | EuDML | MR | Zbl

[5] D. Bertrand, "Relative splitting of one-motives", in Number theory (Tiruchirapalli, 1996), Contemp. Math., vol. 210, Amer. Math. Soc., 1998, p. 3-17. | DOI | MR | Zbl

[6] S. Bosch, W. Lütkebohmert & M. Raynaud - Néron models, Ergebnisse Math. Grenzg. (3), vol. 21, Springer, 1990. | MR | Zbl

[7] J.-B. Bost & K. Künnemann - "Hermitian vector bundles and extension groups on arithmetic schemes. I. Geometry of numbers", preprint arXiv:math.NT/0701343, to appear in Adv. in Math. | MR | Zbl

[8] R.-O. Buchweitz & H. Flenner - "The Atiyah-Chern character yields the semiregularity map as well as the infinitesimal Abel-Jacobi map", in The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), CRM Proc. Lecture Notes, vol. 24, Amer. Math. Soc., 2000, p. 33-46. | DOI | MR | Zbl

[9] R.-O. Buchweitz & H. Flenner, "A semiregularity map for modules and applications to deformations", Composito Math. 137 (2003), p. 135-210. | DOI | MR | Zbl

[10] S.-S. Chern - "Characteristic classes of Hermitian manifolds", Ann. of Math. 47 (1946), p. 85-121. | DOI | MR | Zbl

[11] B. Conrad - "Chow's $K / k$ -image and $K / k$ -trace, and the Lang-Néron theorem", Enseign. Math. 52 (2006), p. 37-108. | MR | Zbl

[12] P. Deligne - "Théorème de Lefschetz et critères de dégénérescence de suites spectrales", Publ. Math. I.H.É.S. 35 (1968), p. 259-278. | EuDML | Numdam | Zbl

[13] P. Deligne, Équations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer, 1970. | MR | Zbl

[14] P. Deligne, "Intersections sur les surfaces régulières", in Groupes de monodromie en géométrie algébrique (SGA 7 II), Lecture Notes in Math., vol. 340, 1973, p. 1-38. | DOI | Zbl

[15] P. Deligne, "Intégration sur un cycle évanescent", Invent. Math. 76 (1984), p. 129-143. | DOI | EuDML | MR | Zbl

[16] W. Fulton - Intersection theory, second ed., Ergebnisse Math. Grenzg.. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 2, Springer, 1998. | MR | Zbl

[17] H. Gillet & C. Soulé - "Arithmetic intersection theory", Publ. Math. I.H.É.S. 72 (1990), p. 93-174. | EuDML | Numdam | MR | Zbl

[18] H. Gillet & C. Soulé, "Characteristic classes for algebraic vector bundles with Hermitian metric. I", Ann. of Math. 131 (1990), p. 163-203. | DOI | MR | Zbl

[19] R. Godement - Topologie algébrique et théorie des faisceaux, Hermann, 1973. | MR | Zbl

[20] P. Griffiths & J. Harris - Principles of algebraic geometry, Wiley-Interscience, 1978. | MR | Zbl

[21] A. Grothendieck - Fondements de la géométrie algébrique. [Extraits du Séminaire Bourbaki, 1957-1962.], Secrétariat mathématique, 1962. | MR | Zbl

[22] A. Grothendieck, "Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. II", Publ. Math. I.H.É.S. 17 (1963). | Numdam | MR | Zbl

[23] A. Grothendieck, "Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas IV", Publ. Math. I.H.É.S. 32 (1967). | EuDML | Numdam | MR | Zbl

[24] M. Hindry, A. Pacheco & R. Wazir - "Fibrations et conjecture de Tate", J. Number Theory 112 (2005), p. 345-368. | DOI | MR | Zbl

[25] L. Illusie - Complexe cotangent et déformations. I, Lecture Notes in Math., vol. 239, Springer, 1971. | MR | Zbl

[26] B. Kahn - "Sur le groupe des classes d'un schéma arithmétique", with an appendix by M. Hindry, Bull. Soc. Math. France 134 (2006), p. 395-415. | DOI | EuDML | Numdam | MR | Zbl

[27] N. M. Katz - "Nilpotent connections and the monodromy theorem: Applications of aresult of Turrittin", Publ. Math. I.H.É.S. 39 (1970), p. 175-232. | DOI | EuDML | Numdam | MR | Zbl

[28] S. L. Kleiman - "Toward a numerical theory of ampleness", Ann. of Math. 84 (1966), p. 293-344. | DOI | MR | Zbl

[29] S. L. Kleiman, "Les théorèmes de finitude pour le foncteur de Picard", in Groupes de monodromie en géométrie algébrique (SGA 6), Lecture Notes in Math., vol. 225, 1971, p. 616-666. | Zbl

[30] S. Kobayashi & K. Nomizu - Foundations of differential geometry. Vol I, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. | MR | Zbl

[31] S. Lang - Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. | MR | Zbl

[32] S. Lang & A. Néron - "Rational points of abelian varieties over function fields", Amer. J. Math. 81 (1959), p. 95-118. | DOI | MR | Zbl

[33] B. Mazur & W. Messing - Universal extensions and one dimensional crystalline cohomology, Lecture Notes in Math., vol. 370, Springer, 1974. | MR | Zbl

[34] W. Messing - "The universal extension of an abelian variety by a vector group", in Symposia Mathematica, Vol. XI (Convegno di Geometria, INDAM, Rome, 1972), Academic Press, 1973, p. 359-372. | MR | Zbl

[35] D. Mumford & J. Fogarty - Geometric invariant theory, second ed., Ergebnisse Math. Grenzg., vol. 34, Springer, 1982. | MR | Zbl

[36] S. Nakano - "On complex analytic vector bundles", J. Math. Soc. Japan 7 (1955), p. 1-12. | DOI | MR | Zbl

[37] P. Sastry & Y. L. L. Tong - "The Grothendieck trace and the de Rham integral", Canad. Math. Bull. 46 (2003), p. 429-440. | DOI | MR | Zbl

[38] T. Schneider - "Zur Theorie der Abelschen Funktionen und Integrale", J. reine angew. Math. 183 (1941), p. 110-128. | EuDML | JFM | MR

[39] J-P. Serre - Groupes algébriques et corps de classes, Publications de l'institut de mathématique de l'université de Nancago, VII. Hermann, Paris, 1959. | MR | Zbl

[40] C. T. Simpson - "Transcendental aspects of the Riemann-Hilbert correspondence", Illinois J. Math. 34 (1990), p. 368-391. | MR | Zbl

[41] M. Spivak - A comprehensive introduction to differential geometry. Vol. II, published by M. Spivak, Brandeis Univ., Waltham, Mass., 1970. | MR | Zbl

[42] M. Waldschmidt - "Nombres transcendants et groupes algébriques", Astérisque 69-70 (1979). | Numdam | Zbl

[43] R. O. J. Wells - Differential analysis on complex manifolds, second ed., Graduate Texts in Math., vol. 65, Springer, 1980. | MR | Zbl

[44] G. Wüstholz - "Algebraische Punkte auf analytischen Untergruppen algebraischer Gruppen", Ann. of Math. 129 (1989), p. 501-517. | DOI | MR | Zbl