An Adams-Riemann-Roch theorem in Arakelov geometry
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Duke Mathematical Journal

An Adams-Riemann-Roch theorem in Arakelov geometry

Damian Roessler

Source: Duke Math. J. Volume 96, Number 1 (1999), 61-126.

First Page PDF: View first page of article (PDF, 78 KB)

Primary Subjects: 14G40
Secondary Subjects: 14C40, 19E08

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077228943
Mathematical Reviews number (MathSciNet): MR1663919
Zentralblatt MATH identifier: 0961.14006
Digital Object Identifier: doi:10.1215/S0012-7094-99-09603-5

References

[1] A. Abbes and T. Bouche, Théorème de Hilbert-Samuel “arithmétique”, Ann. Inst. Fourier (Grenoble) 45 (1995), no. 2, 375–401.
Mathematical Reviews (MathSciNet): MR96e:14024
Zentralblatt MATH: 0818.14011
[2] M. F. Atiyah and D. O. Tall, Group representations, $\lambda$-rings and the $J$-homomorphism, Topology 8 (1969), 253–297.
Mathematical Reviews (MathSciNet): MR39:5702
Zentralblatt MATH: 0159.53301
Digital Object Identifier: doi:10.1016/0040-9383(69)90015-9
[3] Paul Baum, William Fulton, and Robert MacPherson, Riemann-Roch for singular varieties, Inst. Hautes Études Sci. Publ. Math. (1975), no. 45, 101–145.
Mathematical Reviews (MathSciNet): MR54:317
Zentralblatt MATH: 0332.14003
[4] Nicole Berline, Ezra Getzler, and Michèle Vergne, Heat kernels and Dirac operators, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 298, Springer-Verlag, Berlin, 1992.
Mathematical Reviews (MathSciNet): MR94e:58130
Zentralblatt MATH: 0744.58001
[5] P. Berthelot, A. Grothendieck, and L. Illusie, Théorie des intersections et théorème de Riemann-Roch, Lecture Notes in Math., vol. 225, Springer-Verlag, Berlin, 1971.
Mathematical Reviews (MathSciNet): MR50:7133
Zentralblatt MATH: 0218.14001
[6] Jean-Michel Bismut, Superconnection currents and complex immersions, Invent. Math. 99 (1990), no. 1, 59–113.
Mathematical Reviews (MathSciNet): MR91b:58240
Zentralblatt MATH: 0696.58006
Digital Object Identifier: doi:10.1007/BF01234412
[7] Jean-Michel Bismut, Familles d'immersions et formes de torsion analytique en degré supérieur, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 8, 969–974.
Mathematical Reviews (MathSciNet): MR96d:58145
Zentralblatt MATH: 0844.32010
[8] Jean-Michel Bismut, Holomorphic families of immersions and higher analytic torsion forms, Astérisque (1997), no. 244, viii+275, Math. Soc. France, Montrouge.
Mathematical Reviews (MathSciNet): MR2000b:58057
Zentralblatt MATH: 0899.32013
[9]1 J.-M. Bismut, H. Gillet, and C. Soulé, Analytic torsion and holomorphic determinant bundles. I. Bott-Chern forms and analytic torsion, Comm. Math. Phys. 115 (1988), no. 1, 49–78.
Mathematical Reviews (MathSciNet): MR89g:58192a
Zentralblatt MATH: 0651.32017
Digital Object Identifier: doi:10.1007/BF01238853
[9]2 Jean-Michel Bismut, Henri Gillet, and Christophe Soulé, Analytic torsion and holomorphic determinant bundles. II. Direct images and Bott-Chern forms, Comm. Math. Phys. 115 (1988), no. 1, 79–126.
Mathematical Reviews (MathSciNet): MR89g:58192b
Zentralblatt MATH: 0651.32017
Digital Object Identifier: doi:10.1007/BF01238853
[9]3 Jean-Michel Bismut, Henri Gillet, and Christophe Soulé, Analytic torsion and holomorphic determinant bundles. III. Quillen metrics on holomorphic determinants, Comm. Math. Phys. 115 (1988), no. 2, 301–351.
Mathematical Reviews (MathSciNet): MR89g:58192c
Zentralblatt MATH: 0651.32017
Digital Object Identifier: doi:10.1007/BF01238853
[10] J.-M. Bismut, H. Gillet, and C. Soulé, Bott-Chern currents and complex immersions, Duke Math. J. 60 (1990), no. 1, 255–284.
Mathematical Reviews (MathSciNet): MR91d:58239
Zentralblatt MATH: 0697.58005
Digital Object Identifier: doi:10.1215/S0012-7094-90-06009-0
Project Euclid: euclid.dmj/1077297147
[11] Jean-Michel Bismut, Henri Gillet, and Christophe Soulé, Complex immersions and Arakelov geometry, The Grothendieck Festschrift, Vol. I, Progr. Math., vol. 86, Birkhäuser Boston, Boston, MA, 1990, pp. 249–331.
Mathematical Reviews (MathSciNet): MR92a:14019
Zentralblatt MATH: 0744.14015
[12] Jean-Michel Bismut and Kai Köhler, Higher analytic torsion forms for direct images and anomaly formulas, J. Algebraic Geom. 1 (1992), no. 4, 647–684.
Mathematical Reviews (MathSciNet): MR94a:58209
Zentralblatt MATH: 0784.32023
[13] Jean-Michel Bismut and Gilles Lebeau, Complex immersions and Quillen metrics, Inst. Hautes Études Sci. Publ. Math. (1991), no. 74, ii+298 pp. (1992), Soc. Math. France, Paris.
Mathematical Reviews (MathSciNet): MR94a:58205
Zentralblatt MATH: 0784.32010
[14] Jean-Michel Bismut and Éric Vasserot, The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle, Comm. Math. Phys. 125 (1989), no. 2, 355–367.
Mathematical Reviews (MathSciNet): MR91c:58141
Zentralblatt MATH: 0687.32023
Digital Object Identifier: doi:10.1007/BF01217912
[15] Gerd Faltings, Lectures on the arithmetic Riemann-Roch theorem, Annals of Mathematics Studies, vol. 127, Princeton University Press, Princeton, NJ, 1992.
Mathematical Reviews (MathSciNet): MR93f:14006
Zentralblatt MATH: 0744.14016
[16] William Fulton, A note on the arithmetic genus, Amer. J. Math. 101 (1979), no. 6, 1355–1363.
Mathematical Reviews (MathSciNet): MR81k:14007
Zentralblatt MATH: 0497.14002
[17] William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984.
Mathematical Reviews (MathSciNet): MR85k:14004
Zentralblatt MATH: 0541.14005
[18] William Fulton and Serge Lang, Riemann-Roch algebra, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 277, Springer-Verlag, New York, 1985.
Mathematical Reviews (MathSciNet): MR88h:14011
Zentralblatt MATH: 0579.14011
[19] Henri Gillet and Christophe Soulé, Arithmetic intersection theory, Inst. Hautes Études Sci. Publ. Math. (1990), no. 72, 93–174 (1991).
Mathematical Reviews (MathSciNet): MR92d:14016
Zentralblatt MATH: 0741.14012
[20]1 Henri Gillet and Christophe Soulé, Characteristic classes for algebraic vector bundles with Hermitian metric. I, Ann. of Math. (2) 131 (1990), no. 1, 163–203.
Mathematical Reviews (MathSciNet): MR91m:14032a
Zentralblatt MATH: 0715.14018
Digital Object Identifier: doi:10.2307/1971512
JSTOR: links.jstor.org
[20]2 Henri Gillet and Christophe Soulé, Characteristic classes for algebraic vector bundles with Hermitian metric. II, Ann. of Math. (2) 131 (1990), no. 2, 205–238.
Mathematical Reviews (MathSciNet): MR91m:14032b
Zentralblatt MATH: 0715.14006
Digital Object Identifier: doi:10.2307/1971512
JSTOR: links.jstor.org
[21] H. Gillet and C. Soulé, Analytic torsion and the arithmetic Todd genus, Topology 30 (1991), no. 1, 21–54.
Mathematical Reviews (MathSciNet): MR92d:14015
Zentralblatt MATH: 0787.14005
Digital Object Identifier: doi:10.1016/0040-9383(91)90032-Y
[22] Henri Gillet and Christophe Soulé, An arithmetic Riemann-Roch theorem, Invent. Math. 110 (1992), no. 3, 473–543.
Mathematical Reviews (MathSciNet): MR94f:14019
Zentralblatt MATH: 0777.14008
Digital Object Identifier: doi:10.1007/BF01231343
[23] A. Grothendieck, Éléments de géométrie algébrique. I. Le langage des schémas, Inst. Hautes Études Sci. Publ. Math. (1960), no. 4, 228.
Mathematical Reviews (MathSciNet): MR36:177a
Zentralblatt MATH: 0118.36206
[24] Robin Hartshorne, Algebraic geometry, Springer-Verlag, New York, 1977, Grad. Texts in Math.
Mathematical Reviews (MathSciNet): MR57:3116
Zentralblatt MATH: 0367.14001
[25] F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. Die Grundlehren der Mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966.
Mathematical Reviews (MathSciNet): MR34:2573
Zentralblatt MATH: 0138.42001
[26] Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983.
Mathematical Reviews (MathSciNet): MR85g:35002a
Zentralblatt MATH: 0521.35001
[27] S. Lang, Algebra, 3rd ed., Addison-Wesley, Reading, Mass, 1993.
Zentralblatt MATH: 0848.13001
Mathematical Reviews (MathSciNet): MR197234
[28] Yu. I. Manin, Lektsii po algebraicheskoi geometrii. Chast II: $K$-funtstor v algebraicheskoi geometrii, Izdat. Moskov. Univ., Moscow, 1971, (in Russian).
Mathematical Reviews (MathSciNet): MR54:10268
[29] A. Meissner, Arithmetische $K$-theorie, dissertation, Univ. Regensburg, 1993.
[30] Daniel Quillen, Higher algebraic $K$-theory. I, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer, Berlin, 1973, 85–147. Lecture Notes in Math., Vol. 341.
Mathematical Reviews (MathSciNet): MR49:2895
Zentralblatt MATH: 0292.18004
[31] M. Rapoport, N. Schappacher, and P. Schnhder, Beilinson's conjectures on special values of $L$-functions, Perspectives in Mathematics, vol. 4, Academic Press Inc., Boston, MA, 1988.
Mathematical Reviews (MathSciNet): MR89a:14002
Zentralblatt MATH: 0635.00005
[32] Damien Roessler, Lambda structure en $K$-théorie des fibrés algébriques hermitiens, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), no. 3, 251–254.
Mathematical Reviews (MathSciNet): MR96m:14011
Zentralblatt MATH: 0978.19002
[33] Damien Roessler, Un théorème d'Adams-Riemann-Roch en géométrie d'Arakelov, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), no. 8, 749–752.
Mathematical Reviews (MathSciNet): MR97b:14026
Zentralblatt MATH: 0881.19004
[34] D. Roessler, Lambda-structure on Grothendieck groups of hermitian vector bundles, Prépublications de l'Université Paris-Nord, 1996.
[35] C. Soulé, Lectures on Arakelov geometry, Cambridge Studies in Advanced Mathematics, vol. 33, Cambridge University Press, Cambridge, 1992.
Mathematical Reviews (MathSciNet): MR94e:14031
Zentralblatt MATH: 0812.14015
[36] Jean-Louis Verdier, Le théorème de Riemann-Roch pour les intersections complètes, Séminaire de géométrie analytique (École Norm. Sup., Paris, 1974–75), Soc. Math. France, Paris, 1976, 189–228. Astérisque, No. 36-37.
Mathematical Reviews (MathSciNet): MR56:3007
Zentralblatt MATH: 0334.14026

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