Triplets spectraux en géométrie d'Arakelov

Caterina Consani; Matilde Marcolli

doi:10.1016/S1631-073X(02)02569-4

Triplets spectraux en géométrie d'Arakelov
[Spectral triples in Arakelov geometry]

Caterina Consani ¹; Matilde Marcolli ²

¹ Département de mathématiques, Université de Toronto, Canada
² Max-Planck Institut für Mathematik, Bonn, Allemagne

Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 779-784.

Abstract
Résumé

In this Note, we use Connes' theory of spectral triples to provide a connection between Manin's model of the dual graph of the fiber at infinity of an Arakelov surface and the cohomology of the mapping cone of the local monodromy.

Dans cette Note nous employons la théorie des triplets spectraux de Connes pour rapprocher le modèle de Manin du graphe dual de la fibre à l'infini d'une surface d'Arakelov et la cohomologie du cône de la monodromie locale.

Received: 2002-06-27
Revised: 2002-09-26
Published online: 2002-10-20

DOI: 10.1016/S1631-073X(02)02569-4

Author's affiliations:

Caterina Consani ¹; Matilde Marcolli ²

¹ Département de mathématiques, Université de Toronto, Canada
² Max-Planck Institut für Mathematik, Bonn, Allemagne

@article{CRMATH_2002__335_10_779_0,
     author = {Caterina Consani and Matilde Marcolli},
     title = {Triplets spectraux en g\'eom\'etrie {d'Arakelov}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {779--784},
     publisher = {Elsevier},
     volume = {335},
     number = {10},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02569-4},
     language = {fr},
}

TY  - JOUR
AU  - Caterina Consani
AU  - Matilde Marcolli
TI  - Triplets spectraux en géométrie d'Arakelov
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 779
EP  - 784
VL  - 335
IS  - 10
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02569-4
LA  - fr
ID  - CRMATH_2002__335_10_779_0
ER  -

%0 Journal Article
%A Caterina Consani
%A Matilde Marcolli
%T Triplets spectraux en géométrie d'Arakelov
%J Comptes Rendus. Mathématique
%D 2002
%P 779-784
%V 335
%N 10
%I Elsevier
%R 10.1016/S1631-073X(02)02569-4
%G fr
%F CRMATH_2002__335_10_779_0

Caterina Consani; Matilde Marcolli. Triplets spectraux en géométrie d'Arakelov. Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 779-784. doi : 10.1016/S1631-073X(02)02569-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02569-4/

References
Cited by

[1] R. Bowen Hausdorff dimension of quasi-circles, Publ. Math. IHES, Volume 50 (1979), pp. 11-25

[2] M. Boyle; D. Handelman Orbit equivalence, flow equivalence, and ordered cohomology, Israel J. Math, Volume 95 (1996), pp. 169-210

[3] A. Connes Geometry from the spectral point of view, Lett. Math. Phys, Volume 34 (1995) no. 3, pp. 203-238

[4] C. Consani Double complexes and Euler L-factors, Compositio Math, Volume 111 (1998), pp. 323-358

[5] C. Consani; M. Marcolli Non-commutative geometry, dynamics, and ∞-adic Arakelov geometry MPIM preprint (13) 2002 | arXiv

[6] J. Cuntz; W. Krieger A class of $C^{*}$ -algebras and topological Markov chains, Invent. Math, Volume 56 (1980), pp. 251-268

[7] C. Deninger On the Γ-factors attached to motives, Invent. Math, Volume 104 (1991), pp. 245-261

[8] Yu.I. Manin Three-dimensional hyperbolic geometry as ∞-adic Arakelov geometry, Invent. Math, Volume 104 (1991), pp. 223-244

[9] W. Parry; S. Tuncel Classification problems in ergodic theory, London Math. Soc. Lecture Note Ser, 67, 1982

[10] I. Putnam $C^{*}$ -algebras from Smale spaces, Canadian J. Math, Volume 48 (1996) no. 1, pp. 175-195

[11] M. Saito Modules de Hodge polarisable, Publ. Res. Inst. Math. Sci, Volume 24 (1988), pp. 849-995

[12] J.P. Serre Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures), Sém. Delange–Pisot–Poitou, Volume 19 (1969/70)

[13] R.O. Wells Differential Analysis on Complex Manifolds, Springer-Verlag, 1980

Cited by Sources:

Comments - Policy