ε-constants and equivariant Arakelov-Euler characteristics
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 35 (2002) no. 3, pp. 307-352. 
@article{ASENS_2002_4_35_3_307_0,
     author = {Chinburg, Ted and Pappas, Georgios and Taylor, Martin J.},
     title = {$\varepsilon $-constants and equivariant {Arakelov-Euler} characteristics},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {307--352},
     publisher = {Elsevier},
     volume = {Ser. 4, 35},
     number = {3},
     year = {2002},
     doi = {10.1016/s0012-9593(02)01091-1},
     zbl = {1039.11078},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(02)01091-1/}
}
TY  - JOUR
AU  - Chinburg, Ted
AU  - Pappas, Georgios
AU  - Taylor, Martin J.
TI  - $\varepsilon $-constants and equivariant Arakelov-Euler characteristics
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2002
SP  - 307
EP  - 352
VL  - 35
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/s0012-9593(02)01091-1/
DO  - 10.1016/s0012-9593(02)01091-1
LA  - en
ID  - ASENS_2002_4_35_3_307_0
ER  - 
%0 Journal Article
%A Chinburg, Ted
%A Pappas, Georgios
%A Taylor, Martin J.
%T $\varepsilon $-constants and equivariant Arakelov-Euler characteristics
%J Annales scientifiques de l'École Normale Supérieure
%D 2002
%P 307-352
%V 35
%N 3
%I Elsevier
%U http://www.numdam.org/articles/10.1016/s0012-9593(02)01091-1/
%R 10.1016/s0012-9593(02)01091-1
%G en
%F ASENS_2002_4_35_3_307_0
Chinburg, Ted; Pappas, Georgios; Taylor, Martin J. $\varepsilon $-constants and equivariant Arakelov-Euler characteristics. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 35 (2002) no. 3, pp. 307-352. doi : 10.1016/s0012-9593(02)01091-1. http://www.numdam.org/articles/10.1016/s0012-9593(02)01091-1/

[1] Arai K., Conductor formula of Bloch, in tame case, Thesis, University of Tokyo, 2000 (in Japanese).

[2] Bismut J.-M., Equivariant immersions and Quillen metrics, J. Differential Geom. 41 (1995) 53-157. | MR | Zbl

[3] Bloch S., Cycles on Arithmetic schemes and Euler characteristics of curves, in: Proceedings of Symposia in Pure Math., Vol. 46, Part 2, AMS, 421-450. | MR | Zbl

[4] Burns D., Equivariant Tamagawa numbers and Galois module theory I, preprint. | MR

[5] Burns D., Equivariant Tamagawa numbers and Galois module theory II, preprint. | MR

[6] Cassou-Noguès Ph., Taylor M.J., Local root numbers and hermitian Galois structure of rings of integers, Math. Annalen, 263 (1983) 251-261. | MR | Zbl

[7] Chinburg T., Galois structure of de Rham cohomology of tame covers of schemes, Ann. Math. 139 (1994) 443-490, Corrigendum: Ann. Math. 140 (1994) 251. | MR | Zbl

[8] Chinburg T., Erez B., Pappas G., Taylor M.J., ε-constants and the Galois structure of de Rham cohomology, Ann. Math. 146 (1997) 411-473. | Zbl

[9] Chinburg T., Erez B., Pappas G., Taylor M.J., On the ε-constants of arithmetic schemes, Math. Ann. 311 (1998) 377-395. | Zbl

[10] Chinburg T., Erez B., Pappas G., Taylor M.J., On the ε-constants of a variety over a finite field, Amer. J. Math. 119 (1997) 503-522. | Zbl

[11] Chinburg T., Erez B., Pappas G., Taylor M.J., Tame actions of group schemes: integrals and slices, Duke Math. J. 82 (2) (1996) 269-308. | MR | Zbl

[12] Chinburg T., Pappas G., Taylor M.J., ε-constants and the Galois structure of de Rham cohomology II, J. Reine Angew. Math. 519 (2000) 201-230. | Zbl

[13] Chinburg T., Pappas G., Taylor M.J., ε-constants and Arakelov-Euler characteristics, Math. Res. Lett. 7 (2000) 433-446. | Zbl

[14] Chinburg T., Pappas G., Taylor M.J., Duality and hermitian Galois module structure, to appear in the Proc. L.M.S. | MR | Zbl

[15] Deligne P., Les constantes des équations fonctionnelles des fonctions L, in: Lecture Notes in Math., 349, Springer-Verlag, Heidelberg, 1974, pp. 501-597. | MR | Zbl

[16] Fröhlich A., Galois Module Structure of Algebraic Integers, Springer Ergebnisse, Band 1, Folge 3, Springer-Verlag, Heidelberg, 1983. | MR | Zbl

[17] Fröhlich A., Classgroups and Hermitian Modules, Progress in Mathematics, 48, Birkhäuser, Basel, 1984. | MR | Zbl

[18] Fröhlich A., Taylor M.J., Algebraic Number Theory, Cambridge Studies in Advanced Mathematics, 27, Cambridge University Press, 1991. | MR | Zbl

[19] Fulton W., Lang S., Riemann-Roch Algebra, Grundlehren, 277, Springer-Verlag, 1985. | MR | Zbl

[20] Gillet H., Soulé C., Characteristic classes for algebraic vector bundles with hermitian metrics I, II, Ann. Math. 131 (1990) 163-203, 205-238. | MR | Zbl

[21] Gillet H., Soulé C., An arithmetic Riemann-Roch theorem, Invent. Math. 110 (1992) 473-543. | MR | Zbl

[22] Gillet H., Soulé C., Analytic torsion and the arithmetic Todd genus. With an appendix by D. Zagier, Topology 30 (1) (1991) 21-54. | MR | Zbl

[23] Hartshorne R., Residues and Duality, Lecture Notes in Math., 20, Springer-Verlag, 1966. | MR | Zbl

[24] Hecke E., Mathematische Werke, Vandenhoeck and Ruprecht, Göttingen, 1983. | MR | Zbl

[25] Ireland K., Rosen M., A Classical Introduction to Modern Number Theory, Springer Graduate Texts in Mathematics, 84, Springer, New York, 1982. | MR | Zbl

[26] Kato K., Logarithmic structures of Fontaine-Illusie, in: Proc. 1st JAMI Conf., Johns-Hopkins Univ. Press, 1990, pp. 191-224. | MR | Zbl

[27] Knusden F., Mumford D., The projectivity of moduli spaces of stable curves, Math. Scand. 39 (1976) 19-55. | MR | Zbl

[28] Kato K., Saito T., Conductor formula of Bloch, preprint, 2001.

[29] Lang S., Algebraic Number Theory, Addison-Wesley, Reading MA, 1970. | MR | Zbl

[30] Martinet J., Character theory and Artin L-functions, in: Fröhlich A. (Ed.), Algebraic Number Fields, Proc. Durham Symposium 1975, Academic Press, London, 1977. | MR | Zbl

[31] Milne J.S., Étale Cohomology, Princeton University Press, 1980. | MR | Zbl

[32] Ray D.B., Singer I.M., Analytic torsion for complex manifolds, Ann. of Math. (2) 98 (1973) 154-177. | MR | Zbl

[33] Saito T., ε-factor of a tamely ramified sheaf on a variety, Inv. Math. 113 (1993) 389-417. | Zbl

[34] Soulé C., Abramovich D., Burnol J.-F., Kramer J., Lectures on Arakelov Geometry, Cambridge Studies in Advanced Mathematics, 33, Cambridge University Press, Cambridge, 1992. | MR | Zbl

[35] Tate J., Fröhlich A. (Ed.), Thesis in “Algebraic Number Fields”, Academic Press, 1976.

[36] Taylor M.J., On Fröhlich's conjecture for rings of integers of tame extensions, Invent. Math. 63 (1981) 41-79. | MR | Zbl

[37] Taylor M.J., Classgroups of Group Rings, LMS Lecture Notes, 91, Cambridge University Press, Cambridge, 1984. | MR | Zbl

Cité par Sources :