The goal of this paper is to generalize a theorem of Fujiwara (Deligne's conjecture) to the situation appearing in a joint work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our proof is more elementary than the original one and stays in the realm of ordinary algebraic geometry, that is, does not use rigid geometry. We also give a proof of the Lefschetz-Verdier trace formula and of the additivity of filtered trace maps, thus making the paper essentially self-contained.
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Keywords and phrases: Lefschetz trace formula, Deligne’s conjecture AMS Mathematics Subject Classification: Primary: 14F20; Secondary: 11G25, 14G15 The work was supported by the Israel Science Foundation (Grant No. 555/04)
- Deligne's conjecture
- Lefschetz trace formula