Formes de torsion analytique et familles des submersions I
Bulletin de la Société Mathématique de France, Tome 127 (1999) no. 4, p. 541-621
@article{BSMF_1999__127_4_541_0,
     author = {Xiaonan, Ma},
     title = {Formes de torsion analytique et familles des submersions I},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {127},
     number = {4},
     year = {1999},
     pages = {541-621},
     doi = {10.24033/bsmf.2360},
     zbl = {0956.58017},
     mrnumber = {2001j:58059},
     language = {fr},
     url = {http://www.numdam.org/item/BSMF_1999__127_4_541_0}
}
Xiaonan, Ma. Formes de torsion analytique et familles des submersions I. Bulletin de la Société Mathématique de France, Tome 127 (1999) no. 4, pp. 541-621. doi : 10.24033/bsmf.2360. http://www.numdam.org/item/BSMF_1999__127_4_541_0/

[ABoP] Atiyah (M.F.), Bott (R.), Patodi. (V.K.). - On the heat equation and the Index Theorem, Invent. Math., t. 19, 1973, p. 279-330. | MR 58 #31287 | Zbl 0257.58008

[BaFM] Baum (P.), Fulton (W.), Macpherson (R.). - Riemann-Roch for singular varietes, Publ. Math. IHES, t. 45, 1975, p. 101-146. | Numdam | MR 54 #317 | Zbl 0332.14003

[BeGeV] Berline (N.), Getzler (E.), Vergne (M.). - Heat kernels and the Dirac operator. - Grundl. Math. Wiss., 298, Springer, Berlin-Heidelberg-New York, 1992. | MR 94e:58130 | Zbl 0744.58001

[BerB] Berthomieu (A.), Bismut (J.-M.). - Quillen metric and higher analytic torsion forms, J. Reine angew. Math., t. 457, 1994, p. 85-184. | MR 96d:32036 | Zbl 0804.32017

[B1] Bismut (J.-M.). - The Index Theorem for families of Dirac operators : two heat equation proofs, Invent. Math., t. 83, 1986, p. 91-151. | MR 87g:58117 | Zbl 0592.58047

[B3] Bismut (J.-M.). - Koszul complexes, harmonic oscillators and the Todd class, J. Amer. Math. Soc., t. 3, 1990, p. 159-256. | MR 91b:58245 | Zbl 0702.58071

[B4] Bismut (J.-M.). - Families of immersions, and higher analytic torsion, Astérisque, 244, 1997. | MR 2000b:58057 | Zbl 0899.32013

[B5] Bismut (J.-M.). - Familles d'immersions et formes de torsion analytique en degré supérieur, C.R.A.S. Paris, t. 320, série I, 1995, p. 969-974. | MR 96d:58145 | Zbl 0844.32010

[BCh] Bismut (J.-M.), Cheeger (J.). - η-invariants and their adiabatic limits, J. Amer. Math. Soc., t. 2, 1989, p. 33-70. | MR 89k:58269 | Zbl 0671.58037

[BGS1] Bismut (J.-M.), Gillet (H.), Soulé (C.). - Analytic torsion and holomorphic determinant bundles I, Comm. Math. Phys., t. 115, 1988, p. 49-78. | MR 89g:58192a | Zbl 0651.32017

[BGS2] Bismut (J.-M.), Gillet (H.), Soulé (C.). - Analytic torsion and holomorphic determinant bundles II, Comm. Math. Phys., t. 115, 1988, p. 79-126. | MR 89g:58192b | Zbl 0651.32017

[BGS3] Bismut (J.-M.), Gillet (H.), Soulé (C.). - Analytic torsion and holomorphic determinant bundles III, Comm. Math. Phys., t. 115, 1988, p. 301-351. | MR 89g:58192c | Zbl 0651.32017

[BKö] Bismut (J.-M.), Köhler (K.). - Higher analytic torsion forms for direct images and anomaly formulas, J. Alg. Geom., t. 1, 1992, p. 647-684. | MR 94a:58209 | Zbl 0784.32023

[BL] Bismut (J.-M.), Lebeau (G.). - Complex immersions and Quillen metrics, Publ. Math. IHES, 74, 1991, p. 1-297. | Numdam | MR 94a:58205 | Zbl 0784.32010

[BS] Borel (A.), Serre (J.-P.). - Le théorème de Riemann-Roch, Bull. Soc. Math. France, t. 86, 1958, p. 97-136. | Numdam | MR 22 #6817 | Zbl 0091.33004

[CE] Cartan (H.), Eilenberg (S.). - Homological Algebra. - Princeton, 1956. | MR 17,1040e | Zbl 0075.24305

[CP] Charazain (J.), Piriou (A.). - Introduction à la théorie des équations aux dérivées partielles. - Gauthier-Villars, Paris, 1981. | Zbl 0446.35001

[D] Dai (X.). - Adiabatic limits, non multiplicativity of signature and Leray spectal sequence, J. Amer. Math. Soc., t. 4, 1991, p. 265-321. | MR 92f:58169 | Zbl 0736.58039

[F] Faltings (G.). - Lectures on the arithmetic Riemann-Roch Theorem, Ann. Math. Studies, Princeton University Press, 1992. | MR 93f:14006 | Zbl 0744.14016

[Ge] Getzler (E.). - A short proof of the Atiyah-Singer Index Theorem, Topology, t. 25, 1986, p. 111-117. | MR 87h:58207 | Zbl 0607.58040

[GrH] Griffiths (P.), Harris (J.). - Principles of Algebraic Geometry. - Wiley, New-York, 1978. | MR 80b:14001 | Zbl 0408.14001

[Grot] Grothendieck (A.). - Sur quelques points d'algèbre homologique, Tôhoku Math. J., t. 9, 1957, p. 119-221. | MR 21 #1328 | Zbl 0118.26104

[GS1] Gillet (H.), Soulé (C.). - Analytic torsion and the arithmetic Todd genus, Topology, t. 30, 1991, p. 21-54. | MR 92d:14015 | Zbl 0787.14005

[GS2] Gillet (H.), Soulé (C.). - An arithmetic Riemann-Roch Theorem, Invent. Math., t. 110, 1992, p. 473-543. | MR 94f:14019 | Zbl 0777.14008

[KM] Knudsen (P.F.), Mumford (D.). - The projectivity of the moduli space of stable curves I, Preliminaires on "det" and "div", Math. Scand., t. 39, 1976, p. 19-55. | Zbl 0343.14008

[Ma] Ma (Xiaonan). - Formes de torsion analytique et familles de submersions, C. R. Acad. Sciences Paris, t. 324, série I, 1997, p. 205-210. | MR 98b:32026 | Zbl 0880.32015

[Ma1] Ma (Xiaonan). - Formes de torsion analytique et familles de submersions II, à paraître.

[MKS] Mckean (H.), Singer (I.M.). - Curvature and the eigenvalues of the Laplacian, J. Diff. Geom., t. 1, 1967, p. 43-69. | MR 36 #828 | Zbl 0198.44301

[Q1] Quillen (D.). - Higher K-theories I., Springer Lecture Notes in Math., 341, Springer, Berlin, 1973, p. 85-147. | MR 49 #2895 | Zbl 0292.18004

[Q2] Quillen (D.). - Superconnections and the Chern character, Topology, t. 24, 1986, p. 89-95. | MR 86m:58010 | Zbl 0569.58030

[RS] Ray (D.B.), Singer (I.M.). - Analytic torsion for complex manifolds, Ann. of Math., t. 98, 1973, p. 154-177. | MR 52 #4344 | Zbl 0267.32014

[T] Taylor (M.). - Pseudodifferential operators. - Princeton University Press, Princeton, 1981. | MR 82i:35172 | Zbl 0453.47026