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
DOI:
https://doi.org/10.1090/S1079-6762-05-00150-2
Published electronically:
September 28, 2005
MathSciNet review:
2176068
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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.
- Kazuhiro Fujiwara, Rigid geometry, Lefschetz-Verdier trace formula and Deligne’s conjecture, Invent. Math. 127 (1997), no. 3, 489–533. MR 1431137, DOI https://doi.org/10.1007/s002220050129
[KV]KV D. Kazhdan and Y. Varshavsky, On the cohomology of the moduli spaces of $F$-bundles: stable cuspidal Deligne–Lusztig part, in preparation.
- 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
- 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, DOI https://doi.org/10.2307/2946574
- 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
[Fu]Fu K. Fujiwara, Rigid geometry, Lefschetz–Verdier trace formula and Deligne’s conjecture, Invent. Math. 127 (1997), no. 3, 489–533.
[KV]KV D. Kazhdan and Y. Varshavsky, On the cohomology of the moduli spaces of $F$-bundles: stable cuspidal Deligne–Lusztig part, in preparation.
[Il]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.
[Pi]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.
[Ve]Ve J.-L. Verdier, Spécialisation de faisceaux et monodromie modérée, in Analysis and topology on singular spaces, Astérisque 101-102, 1983, pp. 332–364.
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Additional Information
Yakov Varshavsky
Affiliation:
Institute of Mathematics, Hebrew University, Givat-Ram, Jerusalem 91904, Israel
MR Author ID:
638793
Email:
vyakov@math.huji.ac.il
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.
