no. 10
Familles d'immersions holomorphes et formes de torsion analytique équivariantes
Bismut, Jean-Michel1 ; Ma, Xiaonan2
1 Département de mathématique, Université Paris-Sud, bâtiment 425, 91405 Orsay, France
2 Centre de mathématiques, École polytechnique, 91128 Palaiseau cedex, France
Comptes Rendus. Mathématique, Tome 334 (2002) no. 10, pp. 893-897.

Dans cette Note, on étend les résultats sur le comportement par immersion des formes de torsion analytique holomorphes dans un contexte équivariant.

In this Note, we extend the known results on the behaviour by immersion of the holomorphic analytic torsion forms to the equivariant case.

Reçu le :
Accepté le :
DOI : 10.1016/S1631-073X(02)02372-5
Bismut, Jean-Michel 1 ; Ma, Xiaonan 2

1 Département de mathématique, Université Paris-Sud, bâtiment 425, 91405 Orsay, France
2 Centre de mathématiques, École polytechnique, 91128 Palaiseau cedex, France 
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Bismut, Jean-Michel; Ma, Xiaonan. Familles d'immersions holomorphes et formes de torsion analytique équivariantes. Comptes Rendus. Mathématique, Tome 334 (2002) no. 10, pp. 893-897. doi : 10.1016/S1631-073X(02)02372-5. http://www.numdam.org/articles/10.1016/S1631-073X(02)02372-5/

[1] Bismut, J.-M. The Atiyah–Singer index theorem for families of Dirac operators: two heat equation proofs, Invent. Math., Volume 83 (1986) no. 1, pp. 91-151

[2] Bismut, J.-M. Superconnection currents and complex immersions, Invent. Math., Volume 99 (1990) no. 1, pp. 59-113

[3] Bismut, J.-M. Equivariant short exact sequences of vector bundles and their analytic torsion forms, Compositio Math., Volume 93 (1994) no. 3, pp. 291-354

[4] Bismut, J.-M. Equivariant immersions and Quillen metrics, J. Differential Geom., Volume 41 (1995) no. 1, pp. 53-157

[5] Bismut, J.-M. Holomorphic families of immersions and higher analytic torsion forms, Astérisque, Volume 244 (1997), p. viii+275

[6] Bismut, J.-M.; Gillet, H.; Soulé, C. Analytic torsion and holomorphic determinant bundles. I. Bott–Chern forms and analytic torsion, Comm. Math. Phys., Volume 115 (1988) no. 1, pp. 49-78

[7] Bismut, J.-M.; Gillet, H.; Soulé, C. Analytic torsion and holomorphic determinant bundles. II. Direct images and Bott–Chern forms, Comm. Math. Phys., Volume 115 (1988) no. 1, pp. 79-126

[8] Bismut, J.-M.; Gillet, H.; Soulé, C. Analytic torsion and holomorphic determinant bundles. III. Quillen metrics on holomorphic determinants, Comm. Math. Phys., Volume 115 (1988) no. 2, pp. 301-351

[9] Bismut, J.-M.; Köhler, K. Higher analytic torsion forms for direct images and anomaly formulas, J. Algebraic Geom., Volume 1 (1992) no. 4, pp. 647-684

[10] Bismut, J.-M.; Lebeau, G. Complex immersions and Quillen metrics, Inst. Hautes Études Sci. Publ. Math., Volume 74 (1991), p. ii+298

[11] J.-M. Bismut, X. Ma, Holomorphic immersions and equivariant torsion forms, Preprint Université Paris-Sud, Orsay, 2002

[12] Gillet, H.; Soulé, C. Analytic torsion and the arithmetic Todd genus, Topology, Volume 30 (1991) no. 1, pp. 21-54 (With an appendix by D. Zagier)

[13] Gillet, H.; Soulé, C. An arithmetic Riemann–Roch theorem, Invent. Math., Volume 110 (1992) no. 3, pp. 473-543

[14] K. Köhler, A Hirzeburch proportionality principle in Arakelov geometry, Preprint, 2002

[15] Köhler, K.; Roessler, D. A fixed point formula of Lefschetz type in Arakelov geometry I: statement and proof, Invent. Math., Volume 145 (2001) no. 2, pp. 333-396

[16] Köhler, K.; Roessler, D. A fixed point formula of Lefschetz type in Arakelov geometry II: a residual formula, Ann. Inst. Fourier, Volume 52 (2002), pp. 81-103

[17] Ma, X. Submersions and equivariant Quillen metrics, Ann. Inst. Fourier (Grenoble), Volume 50 (2000) no. 5, pp. 1539-1588

[18] V. Maillot, D. Roessler, Conjectures sur les dérivées logarithmiques des fonctions L d'Artin aux entiers négatifs, Preprint, 2002

[19] Quillen, D. Determinants of Cauchy–Riemann operators on Riemann surfaces, Functional Anal. Appl., Volume 19 (1985) no. 1, pp. 31-34

[20] Quillen, D. Superconnections and the Chern character, Topology, Volume 24 (1985) no. 1, pp. 89-95

[21] Ray, D.B.; Singer, I.M. Analytic torsion for complex manifolds, Ann. of Math. (2), Volume 98 (1973), pp. 154-177

[22] Roessler, D. An Adams–Riemann–Roch theorem in Arakelov geometry, Duke Math. J., Volume 96 (1999) no. 1, pp. 61-126

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