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A proof of a generalization of Deligne's conjecture

Author(s): Yakov Varshavsky
Journal: Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 78-88.
MSC (2000): Primary 14F20; Secondary 11G25, 14G15
Posted: September 28, 2005
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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:

[Fu]
K. Fujiwara, Rigid geometry, Lefschetz-Verdier trace formula and Deligne's conjecture, Invent. Math. 127 (1997), no. 3, 489-533. MR 1431137 (99c:14030)

[KV]
D. Kazhdan and Y. Varshavsky, On the cohomology of the moduli spaces of $ F$-bundles: stable cuspidal Deligne-Lusztig part, in preparation.

[Il]
L. Illusie, Formule de Lefschetz, in Coholologie $ \ell$-adique et fonctions $ L$, SGA5, Lecture Notes in Mathematics 589, Springer-Verlag, 1977, pp. 73-137. MR 0491704 (58:10907)

[Pi]
R. Pink, On the calculation of local terms in the Lefschetz-Verdier trace formula and its application to a conjecture of Deligne, Ann. of Math. 135 (1992), no. 3, 483-525. MR 1166642 (93m:14017)

[Ve]
J.-L. Verdier, Spécialisation de faisceaux et monodromie modérée, in Analysis and topology on singular spaces, Astérisque 101-102, 1983, pp. 332-364. MR 0737938 (86f:32010)

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Additional Information:

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

DOI: 10.1090/S1079-6762-05-00150-2
PII: S 1079-6762(05)00150-2
Keywords: Lefschetz trace formula, Deligne's conjecture
Received by editor(s): May 16, 2005
Posted: September 28, 2005
Additional Notes: The work was supported by the Israel Science Foundation (Grant No. 555/04)
Communicated by: Svetlana Katok
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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