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arXiv 2003.068152020-03math.AG

Local terms for transversal intersections

Yakov Varshavsky

备注：: 18 pages, comments are welcome. v3: minor revision, some cross-references corrected

英文摘要：

The goal of this note is to show that in the case of transversal intersections the "true local terms" appearing in the Lefschetz trace formula equal to the "naive local terms". To prove the result we extend the method of [Va], where the case of contracting correspondences is treated. Our new ingredients are the observation of Verdier that specialization of any etale sheaf to the normal cone is monodromic and the assertion that in some cases local terms are "constant in families". As an application, we get a generalization of the Deligne-Lusztig trace formula.

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