Remote Access Electronic Research Announcements

Electronic Research Announcements

ISSN 1079-6762

 

 

A proof of a generalization of Deligne's conjecture


Author: Yakov Varshavsky
Journal: Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 78-88
MSC (2000): Primary 14F20; Secondary 11G25, 14G15
Published electronically: September 28, 2005
MathSciNet review: 2176068
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The goal of this paper is to give a simple proof of Deligne's conjecture on the Lefschetz trace formula (proven by Fujiwara) and to generalize it to the situation appearing in the forthcoming joint paper with D. Kazhdan. Our proof holds in the realm of ordinary algebraic geometry and does not use rigid geometry.


References [Enhancements On Off] (What's this?)

  • [Fu] Kazuhiro Fujiwara, Rigid geometry, Lefschetz-Verdier trace formula and Deligne’s conjecture, Invent. Math. 127 (1997), no. 3, 489–533. MR 1431137, 10.1007/s002220050129
  • [KV] D. Kazhdan and Y. Varshavsky, On the cohomology of the moduli spaces of $ F$-bundles: stable cuspidal Deligne-Lusztig part, in preparation.
  • [Il] Cohomologie 𝑙-adique et fonctions 𝐿, Lecture Notes in Mathematics, Vol. 589, Springer-Verlag, Berlin-New York, 1977 (French). Séminaire de Géometrie Algébrique du Bois-Marie 1965–1966 (SGA 5); Edité par Luc Illusie. MR 0491704
  • [Pi] Richard Pink, On the calculation of local terms in the Lefschetz-Verdier trace formula and its application to a conjecture of Deligne, Ann. of Math. (2) 135 (1992), no. 3, 483–525. MR 1166642, 10.2307/2946574
  • [Ve] J.-L. Verdier, Spécialisation de faisceaux et monodromie modérée, Analysis and topology on singular spaces, II, III (Luminy, 1981) Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 332–364 (French). MR 737938

Similar Articles

Retrieve articles in Electronic Research Announcements of the American Mathematical Society with MSC (2000): 14F20, 11G25, 14G15

Retrieve articles in all journals with MSC (2000): 14F20, 11G25, 14G15


Additional Information

Yakov Varshavsky
Affiliation: Institute of Mathematics, Hebrew University, Givat-Ram, Jerusalem 91904, Israel
Email: vyakov@math.huji.ac.il

DOI: http://dx.doi.org/10.1090/S1079-6762-05-00150-2
Keywords: Lefschetz trace formula, Deligne's conjecture
Received by editor(s): May 16, 2005
Published electronically: September 28, 2005
Additional Notes: The work was supported by the Israel Science Foundation (Grant No. 555/04)
Communicated by: Svetlana Katok
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.