Dans cette Note, on annonce l'annulation des formes de torsion analytique holomorphes du complexe de de Rham relatif d'une fibration équivariante.
In this Note, we announce the vanishing of the holomorphic torsion forms of the relative de Rham complex of an equivariant fibration.
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@article{CRMATH_2002__335_3_243_0, author = {Bismut, Jean-Michel}, title = {Les formes de torsion holomorphes du complexe de de {Rham}}, journal = {Comptes Rendus. Math\'ematique}, pages = {243--247}, publisher = {Elsevier}, volume = {335}, number = {3}, year = {2002}, doi = {10.1016/S1631-073X(02)02469-X}, language = {fr}, url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02469-X/} }
TY - JOUR AU - Bismut, Jean-Michel TI - Les formes de torsion holomorphes du complexe de de Rham JO - Comptes Rendus. Mathématique PY - 2002 SP - 243 EP - 247 VL - 335 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02469-X/ DO - 10.1016/S1631-073X(02)02469-X LA - fr ID - CRMATH_2002__335_3_243_0 ER -
%0 Journal Article %A Bismut, Jean-Michel %T Les formes de torsion holomorphes du complexe de de Rham %J Comptes Rendus. Mathématique %D 2002 %P 243-247 %V 335 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02469-X/ %R 10.1016/S1631-073X(02)02469-X %G fr %F CRMATH_2002__335_3_243_0
Bismut, Jean-Michel. Les formes de torsion holomorphes du complexe de de Rham. Comptes Rendus. Mathématique, Tome 335 (2002) no. 3, pp. 243-247. doi : 10.1016/S1631-073X(02)02469-X. http://www.numdam.org/articles/10.1016/S1631-073X(02)02469-X/
[1] A Lefschetz fixed point formula for elliptic complexes. I, Ann. of Math., Volume 86 (1967) no. 2, pp. 374-407
[2] A Lefschetz fixed point formula for elliptic complexes. II. Applications, Ann. of Math., Volume 88 (1968) no. 2, pp. 451-491
[3] The Atiyah–Singer index theorem for families of Dirac operators: two heat equation proofs, Invent. Math., Volume 83 (1986) no. 1, pp. 91-151
[4] Holomorphic families of immersions and higher analytic torsion forms, Astérisque, Volume 244 (1997), p. viii+275
[5] J.-M. Bismut, Holomorphic and de Rham torsion, Preprint Université Paris-Sud, Orsay, 2002
[6] Analytic torsion and holomorphic determinant bundles. II. Direct images and Bott–Chern forms, Comm. Math. Phys., Volume 115 (1988) no. 1, pp. 79-126
[7] Higher analytic torsion forms for direct images and anomaly formulas, J. Algebraic Geom., Volume 1 (1992) no. 4, pp. 647-684
[8] Flat vector bundles, direct images and higher real analytic torsion, J. Amer. Math. Soc., Volume 8 (1995) no. 2, pp. 291-363
[9] J.-M. Bismut, X. Ma, Holomorphic immersions and equivariant torsion forms, Preprint Université Paris-Sud, Orsay, 2002
[10] An arithmetic Riemann–Roch theorem, Invent. Math., Volume 110 (1992) no. 3, pp. 473-543
[11] Submersions and equivariant Quillen metrics, Ann. Inst. Fourier (Grenoble), Volume 50 (2000) no. 5, pp. 1539-1588
[12] V. Maillot, D. Roessler, Conjectures sur les dérivées logarithmiques des fonctions L d'Artin aux entiers négatifs, Preprint, 2002
[13] Superconnections and the Chern character, Topology, Volume 24 (1985) no. 1, pp. 89-95
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