Complex immersions and Quillen metrics
Bismut, Jean-Michel ; Lebeau, Gilles
Publications Mathématiques de l'IHÉS, Tome 74 (1991), p. 1-298 / Harvested from Numdam
@article{PMIHES_1991__74__1_0,
     author = {Bismut, Jean-Michel and Lebeau, Gilles},
     title = {Complex immersions and Quillen metrics},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {74},
     year = {1991},
     pages = {1-298},
     mrnumber = {94a:58205},
     zbl = {0784.32010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1991__74__1_0}
}
Bismut, Jean-Michel; Lebeau, Gilles. Complex immersions and Quillen metrics. Publications Mathématiques de l'IHÉS, Tome 74 (1991) pp. 1-298. http://gdmltest.u-ga.fr/item/PMIHES_1991__74__1_0/

[AlGBMNV] Alvarez-Gaumé L., Bost J. B., Moore G., Nelson P., Vafa C., Bosonization on higher genus Riemann surfaces, Comm. Math. Phys., 112 (1987), 503-552. | MR 88j:81061 | Zbl 0647.14019

[Ar] Arakelov S., Intersection theory of divisors on an arithmetic surface, Izv. Akad. Nauk SSSR., Ser. Mat., 38 (1974), n° 6. AMS Translation, 8 (1974), n° 6, 1167-1180. | MR 57 #12505 | Zbl 0355.14002

[ABo] Atiyah M. F., Bott R, A Lefschetz fixed point formula for elliptic complexes, I, Ann. Math., 86 (1967), 374-407 ; II, Ann. of Math., 88 (1968), 451-491. | MR 35 #3701 | Zbl 0161.43201

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

[AS] Atiyah M. F., Singer I. M., The index of elliptic operators, III, Ann. of Math., 87 (1968), 546-604. | MR 38 #5245 | Zbl 0164.24301

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

[BeV] Berline N., Vergne M., A proof of Bismut local index theorem for a family of Dirac operators, Topology, 26 (1987), 435-463. | MR 88m:58179 | Zbl 0636.58030

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

[B2] Bismut J. M., Superconnection currents and complex immersions, Invent. Math., 99 (1990), 59-113. | MR 91b:58240 | Zbl 0696.58006

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

[B4] Bismut J. M., Large deviations and the Malliavin calculus, Prog. Math. n° 45, Basel-Boston-Stuttgart, Birkhäuser, 1984. | MR 86f:58150 | Zbl 0537.35003

[B5] Bismut J. M., The Atiyah-Singer Index Theorems : a probabilistic approach, I, J. Funct. Anal., 57 (1984), 56-99. | MR 86g:58128a | Zbl 0538.58033

[B6] Bismut J. M., Demailly's asymptotic Morse inequalities : a heat equation proof, J. Funct. Anal., 72 (1987), 263-278. | MR 88j:58131 | Zbl 0649.58030

[B7] Bismut J. M., The Witten complex and the degenerate Morse inequalities, J. of Diff. Geom., 23 (1986), 207-240. | MR 87m:58169 | Zbl 0608.58038

[BGS1] Bismut J. M., Gillet H., Soulé C., Analytic torsion and holomorphic determinant bundles, I, Comm. Math. Phys., 115 (1988), 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., 115 (1988), 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., 115 (1988), 301-351. | MR 89g:58192c | Zbl 0651.32017

[BGS4] Bismut J. M., Gillet H., Soulé C., Bott-Chern currents and complex immersions. Duke Math. Journal, 60 (1990), 255-284. | MR 91d:58239 | Zbl 0697.58005

[BGS5] Bismut J. M., Gillet H., Soulé C., Complex immersions and Arakelov geometry, The Grothendieck Festschrift, P. Cartier and al. ed., pp. 249-331. Prog. Math. n° 86, Boston-Basel-Berlin, Birkhaüser, 1990. | MR 92a:14019 | Zbl 0744.14015

[BL] Bismut J. M., Lebeau G., Immersions complexes et métriques de Quillen. C.R. Acad. Sci. Paris, 309, Série I (1989), 487-491. | MR 91k:58138 | Zbl 0681.53034

[BoC] Bott R., Chern S. S., Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections, Acta Math., 114 (1968), 71-112. | MR 32 #3070 | Zbl 0148.31906

[CP] Chazarain J., Piriou A., Introduction à la théorie des équations aux dérivées partielles linéaires, Paris, Gauthier-Villars, 1981. | MR 82i:35001 | Zbl 0446.35001

[Ch] Cheeger J., Analytic torsion and the heat equation, Ann. of Math., 109 (1979), 259-322. | MR 80j:58065a | Zbl 0412.58026

[De] Deligne P., Le déterminant de la cohomologie, Contemporary mathematics, 67 (1987), 93-177. | MR 89b:32038 | Zbl 0629.14008

[Do] Donaldson S., Anti-self dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc., 50 (1985), 1-26. | MR 86h:58038 | Zbl 0529.53018

[Dy] Dynkin E. B., Diffusion of tensors, Soviet Math Doklady, 9 (1968), 532-535. | MR 38 #2840 | Zbl 0188.27002

[E] Eilenberg S., Homological dimension and local syzygies, Ann. of Math., 64 (1956), 328-336. | MR 18,558c | Zbl 0073.26003

[F] Faltings G., Calculus on arithmetic surfaces, Ann. of Math., 119 (1984), 387-424. | MR 86e:14009 | Zbl 0559.14005

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

[GS1] Gillet H., Soulé C., Arithmetic Intersection Theory, Publ. Math. IHES, 72 (1990), 93-174. | Numdam | MR 92d:14016 | Zbl 0741.14012

[GS2] Gillet H., Soulé C., Characteristic classes for algebraic vector bundles with Hermitian metric, Ann. of Math., I, 131 (1990), 163-203, II, 131 (1990), 205-238. | MR 91m:14032a | Zbl 0715.14018

[GS3] Gillet H., Soulé C., Analytic torsion and the arithmetic Todd genus. Topology, 30 (1991), 21-54. | MR 92d:14015 | Zbl 0787.14005

[GS4] Gillet H., Soulé C., Un théorème de Rieman-Roch-Grothendieck arithmétique. C.R. Acad. Sci. Paris, 309, Série I (1989), 929-932. | MR 91m:14031 | Zbl 0732.14002

[GlJ] Glimm J., Jaffe A., Quantum physics, Berlin, Heidelberg, New York, Springer, 1987. | MR 89k:81001 | Zbl 0461.46051

[GrH] Griffiths P., Harris J., Principles of algebraic geometry, New York, Wiley, 1978. | MR 80b:14001 | Zbl 0408.14001

[HeSj1] Helffer B., Sjöstrand J., Puits multiples en limite semi-classique. IV, Étude du complexe de Witten, Comm. in P.D.E., 10 (1985), 245-340. | Zbl 0597.35024

[HeSj2] Helffer B., Sjöstrand J., Puits multiples en limite semi-classique. VI, Cas des puits sous-variétés, Ann. Inst. H. Poincaré, 46 (1987), 353-372. | Numdam | Zbl 0648.35027

[HeSj3] Helffer B., Sjöstrand J., A proof of the Bott inequalities, in Algebraic Analysis, Vol. I, M. Kashiwara, T. Kawai ed., New York, Academic Press, 1988, 171-183. | MR 90g:58018 | Zbl 0693.58019

[H] Hirzebruch F., Arithmetic genera and the theorem of Riemann-Roch for algebraic varieties. Proc. Natl. Acad. Sci., USA, 40 (1954), 110-114. | MR 17,535a | Zbl 0055.38803

[Hi] Hitchin N. J., Harmonic spinors. Adv. in Math., 14 (1974), 1-55. | MR 50 #11332 | Zbl 0284.58016

[I] Itô K., Stochastic parallel displacement, in Probabilistic methods in differential equations, Lecture Notes in Mathematics n° 45, Berlin, Heidelberg, New York, Springer, 1975, 1-7. | MR 52 #15704 | Zbl 0308.60027

[KnM] Knudsen F. F., Mumford D., The projectivity of the moduli space of stable curves, I, Preliminaries on "det" and "div", Math. Scand., 39 (1976), 19-55. | MR 55 #10465 | Zbl 0343.14008

[K] Kobayashi S., Differential geometry of complex vector bundles, Iwanami Shoten and Princeton University Press, 1987. | MR 89e:53100 | Zbl 0708.53002

[KN] Kobayashi S., Nomizu K., Foundations of differential geometry, II, New York, Interscience, 1969. | MR 38 #6501 | Zbl 0175.48504

[La] Lang S., Introduction to Arakelov theory, Berlin, Heidelberg, New York, Springer, 1988. | MR 89m:11059 | Zbl 0667.14001

[Li] Lichnerowicz A., Spineurs harmoniques, C.R. Acad. Sci. Paris, Série A, 257 (1963), 7-9. | MR 27 #6218 | Zbl 0136.18401

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

[Mü] Müller W., Analytic torsion and R. torsion of Riemannian manifolds, Adv. in Math., 28 (1978), 233-305. | MR 80j:58065b | Zbl 0395.57011

[Q1] Quillen D., Superconnections and the Chern character, Topology, 24 (1985), 89-95. | MR 86m:58010 | Zbl 0569.58030

[Q2] Quillen D., Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl., 14 (1985), 31-34. | MR 86g:32035 | Zbl 0603.32016

[RS1] Ray D. B., Singer I. M., R.torsion and the Laplacian on Riemannian manifolds, Adv. in Math., 7 (1971), 145-210. | MR 45 #4447 | Zbl 0239.58014

[RS2] Ray D. B., Singer I. M., Analytic torsion for complex manifolds, Ann. of Math., 98 (1973), 154-177. | MR 52 #4344 | Zbl 0267.32014

[ReSi] Reed M., Simon B., Methods of modern mathematical physics, Vol. I, Functional Analysis, New York, Academic Press, 1972. Vol. II, Fourier analysis, self-adjointness, New York, Academic Press, 1975. | Zbl 0242.46001

[Se] Seeley R. T., Complex powers of an elliptic operator. Proc. Symp. Pure and Appl. Math. AMS, 10 (1967), 288-307. | MR 38 #6220 | Zbl 0159.15504

[Ser] Serre J. P., Algèbre locale. Multiplicités. Lecture Notes in Math. n° 11, Berlin, Heidelberg, New York, Springer, 1965. | MR 34 #1352 | Zbl 0142.28603

[Ta] Tangerman F. M., To appear.

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

[W] Witten E., Supersymmetry and Morse theory, J. Differential Geom., 17 (1982), 661-692. | MR 84b:58111 | Zbl 0499.53056