@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://www.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://www.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://www.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://www.numdam.org/item/AST_2009__327__361_0/
[1] Calcul différentiel et classes caractéristiques en géométrie algébrique, Travaux en Cours, vol. 38, Hermann, 1989. | MR | Zbl
& -[2] Complex analytic connections in fibre bundles", Trans. Amer. Math. Soc. 85 (1957), p. 181-207. | DOI | MR | Zbl
- "[3] Logarithmic forms and Diophantine geometry", New Mathematical Monographs, Cambridge Univ. Press, 2007. | MR | Zbl
& - "[4] Points rationnels sur les sous-groupes compacts des groupes algébriques", Experiment. Math. 4 (1995), p. 145-151. | DOI | EuDML | MR | Zbl
- "[5] 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] Néron models, Ergebnisse Math. Grenzg. (3), vol. 21, Springer, 1990. | MR | Zbl
, & -[7] 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] 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] A semiregularity map for modules and applications to deformations", Composito Math. 137 (2003), p. 135-210. | DOI | MR | Zbl
& , "[10] Characteristic classes of Hermitian manifolds", Ann. of Math. 47 (1946), p. 85-121. | DOI | MR | Zbl
- "[11] Chow's -image and -trace, and the Lang-Néron theorem", Enseign. Math. 52 (2006), p. 37-108. | MR | Zbl
- "[12] 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] Équations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer, 1970. | MR | Zbl
,[14] 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] Intégration sur un cycle évanescent", Invent. Math. 76 (1984), p. 129-143. | DOI | EuDML | MR | Zbl
, "[16] Intersection theory, second ed., Ergebnisse Math. Grenzg.. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 2, Springer, 1998. | MR | Zbl
-[17] Arithmetic intersection theory", Publ. Math. I.H.É.S. 72 (1990), p. 93-174. | EuDML | Numdam | MR | Zbl
& - "[18] Characteristic classes for algebraic vector bundles with Hermitian metric. I", Ann. of Math. 131 (1990), p. 163-203. | DOI | MR | Zbl
& , "[19] Topologie algébrique et théorie des faisceaux, Hermann, 1973. | MR | Zbl
-[20] Principles of algebraic geometry, Wiley-Interscience, 1978. | MR | Zbl
& -[21] Fondements de la géométrie algébrique. [Extraits du Séminaire Bourbaki, 1957-1962.], Secrétariat mathématique, 1962. | MR | Zbl
-[22] Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. II", Publ. Math. I.H.É.S. 17 (1963). | Numdam | MR | Zbl
, "[23] 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] Fibrations et conjecture de Tate", J. Number Theory 112 (2005), p. 345-368. | DOI | MR | Zbl
, & - "[25] Complexe cotangent et déformations. I, Lecture Notes in Math., vol. 239, Springer, 1971. | MR | Zbl
-[26] 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] 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] Toward a numerical theory of ampleness", Ann. of Math. 84 (1966), p. 293-344. | DOI | MR | Zbl
- "[29] 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] Foundations of differential geometry. Vol I, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. | MR | Zbl
& -[31] Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. | MR | Zbl
-[32] Rational points of abelian varieties over function fields", Amer. J. Math. 81 (1959), p. 95-118. | DOI | MR | Zbl
& - "[33] Universal extensions and one dimensional crystalline cohomology, Lecture Notes in Math., vol. 370, Springer, 1974. | MR | Zbl
& -[34] 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] Geometric invariant theory, second ed., Ergebnisse Math. Grenzg., vol. 34, Springer, 1982. | MR | Zbl
& -[36] On complex analytic vector bundles", J. Math. Soc. Japan 7 (1955), p. 1-12. | DOI | MR | Zbl
- "[37] The Grothendieck trace and the de Rham integral", Canad. Math. Bull. 46 (2003), p. 429-440. | DOI | MR | Zbl
& - "[38] Zur Theorie der Abelschen Funktionen und Integrale", J. reine angew. Math. 183 (1941), p. 110-128. | EuDML | JFM | MR
- "[39] Groupes algébriques et corps de classes, Publications de l'institut de mathématique de l'université de Nancago, VII. Hermann, Paris, 1959. | MR | Zbl
-[40] Transcendental aspects of the Riemann-Hilbert correspondence", Illinois J. Math. 34 (1990), p. 368-391. | MR | Zbl
- "[41] A comprehensive introduction to differential geometry. Vol. II, published by M. Spivak, Brandeis Univ., Waltham, Mass., 1970. | MR | Zbl
-[42] Nombres transcendants et groupes algébriques", Astérisque 69-70 (1979). | Numdam | Zbl
- "[43] Differential analysis on complex manifolds, second ed., Graduate Texts in Math., vol. 65, Springer, 1980. | MR | Zbl
-[44] Algebraische Punkte auf analytischen Untergruppen algebraischer Gruppen", Ann. of Math. 129 (1989), p. 501-517. | DOI | MR | Zbl
- "