Formes automorphes et théorèmes de Riemann-Roch arithmétiques

From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 328 (2009), 17 p.

MR 2674879 | Zbl 1232.14016

@incollection{AST_2009__328__237_0,
     author = {Maillot, Vincent and R\"ossler, Damian},
     title = {Formes automorphes et th\'eor\`emes de Riemann-Roch arithm\'etiques},
     booktitle = {From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut},
     editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {328},
     year = {2009},
     zbl = {1232.14016},
     mrnumber = {2674879},
     language = {fr},
     url = {http://www.numdam.org/item/AST_2009__328__237_0/}
}

Maillot, Vincent; Rössler, Damian. Formes automorphes et théorèmes de Riemann-Roch arithmétiques, dans From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 328 (2009), 17 p. http://www.numdam.org/item/AST_2009__328__237_0/

Bibliographie

[1] Théorie des intersections et théorème de Riemann-Roch - in Séminaire de Géométrie Algébrique du Bois-Marie 1966-1967 (SGA 6) (P. Berthelot, A. Grothendieck & L. Illu-sie, éds.), Lecture Notes in Math., vol. 225, Springer, 1971. | MR 354655 | Zbl 0218.14001

[2] D. Abramovich - Subvarieties of semiabelian varieties, Compositio Math. 90 (1994), p. 37-52. | EuDML 90266 | Numdam | MR 1266493 | Zbl 0814.14041

[3] W. P. Barth, K. Hulek, C. A. M. Peters & A. Van De Ven - Compact complex surfaces, 2e éd., Ergebnisse Math. Grenzg. 3. Folge, vol. 4, Springer, 2004. | MR 2030225 | Zbl 1036.14016

[4] J.-M. Bismut & K. Köhler - Higher analytic torsion forms for direct images and anomaly formulas, J. Algebraic Geom. 1 (1992), p. 647-684. | MR 1174905 | Zbl 0784.32023

[5] R. E. Borcherds - The moduli space of Enriques surfaces and the fake monster Lie superalgebra, Topology 35 (1996), p. 699-710. | Article | MR 1396773 | Zbl 0886.14015

[6] J.-B. Bost - Intrinsic heights of stable varieties and abelian varieties, Duke Math. J. 82 (1996), p. 21-70. | Article | MR 1387221 | Zbl 0867.14010

[7] W. Fulton - Intersection theory, 2e éd., Ergebnisse Math. Grenzg.. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 2, Springer, 1998. | MR 1644323 | Zbl 0885.14002

[9] H. Gillet & C. Soulé - Characteristic classes for algebraic vector bundles with Hermitian metric. I, Ann. of Math. 131 (1990), p. 163-203. | Article | MR 1038362 | Zbl 0715.14018

[10]H. Gillet, D. Rössler & C. Soulé, Characteristic classes for algebraic vector bundles with Hermitian metric. II, Ann. of Math. 131 (1990), p. 205-238. | Article | MR 1043268 | Zbl 0715.14006

[11] H. Gillet, D. Rössler & C. Soulé, An arithmetic Riemann-Roch theorem, Invent. Math. 110 (1992), p. 473-543. | Article | EuDML 144061 | MR 1189489 | Zbl 0777.14008

[12] F. Hirzebruch - Topological methods in algebraic geometry, Grundl. Math. Wiss., vol. 131, Springer, 1966. | MR 202713 | Zbl 0138.42001

[13] K. Köhler & D. Rössler - A fixed point formula of Lefschetz type in Arakelov geometry. I. Statement and proof, Invent. Math. 145 (2001), p. 333-396. | Article | MR 1872550 | Zbl 0999.14002

[14] J. Kramer & R. Salvati Manni - An integral characterizing the Andreotti-Mayer locus, Abh. Math. Sem. Univ. Hamburg 72 (2002), p. 47-57. | Article | MR 1941546 | Zbl 1011.11029

[15] V. Maillot & D. Rössler - On the periods of motives with complex multiplication and a conjecture of Gross-Deligne, Ann. of Math. 160 (2004), p. 727-754. | Article | MR 2123937 | Zbl 1077.14032

[16] L. Moret-Bailly - Sur l'équation fonctionnelle de la fonction thêta de Riemann, Compositio Math. 75 (1990), p. 203-217. | EuDML 90034 | Numdam | MR 1065206 | Zbl 0728.14039

[17] C. Mourougane - Computations of Bott-Chern classes on $𝐏 (E)$ , Duke Math. J. 124 (2004), p. 389-420. | Article | MR 2079253 | Zbl 1064.14022

[18] D. Mumford - Tata lectures on theta. I, Modern Birkhäuser Classics, Birkhäuser Boston Inc., 2007. | MR 2352717 | Zbl 1112.14002

[19] G. Pappas - Grothendieck-Riemann-Roch and the moduli of Enriques surfaces, Math. Res. Lett. 15 (2008), p. 117-120. | Article | MR 2367178 | Zbl 1143.14029

[20] D. B. Ray & I. M. Singer - Analytic torsion for complex manifolds, Ann. of Math. 98 (1973), p. 154-177. | Article | MR 383463 | Zbl 0267.32014

[21] D. Rössler - An Adams-Riemann-Roch theorem in Arakelov geometry, Duke Math. J. 96 (1999), p. 61-126. | Article | MR 1663919 | Zbl 0961.14006

[22] D. Rössler, Riemann-Roch formulae in Arakelov geometry and applications. (2006), lecture notes.

[23] H. Tamvakis - Bott-Chern forms and arithmetic intersections, Enseign. Math. 43 (1997), p. 33-54. | MR 1460121 | Zbl 0917.32025

[24] R. W. Thomason - Une formule de Lefschetz en $K$ -théorie équivariante algébrique, Duke Math. J. 68 (1992), p. 447-462. | Article | MR 1194949 | Zbl 0813.19002

[25] J. R. O. Wells - Differential analysis on complex manifolds, 3e éd., Graduate Texts in Math., vol. 65, Springer, 2008. | MR 2359489 | Zbl 1131.32001

[26] K.-I. Yoshikawa - Discriminant of theta divisors and Quillen metrics, J. Differential Geom. 52 (1999), p. 73-115. | Article | MR 1743687 | Zbl 1033.58029

[27] K.-I. Yoshikawa, K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space, Invent. Math. 156 (2004), p. 53-117. | Article | MR 2047658 | Zbl 1058.58013