Local terms for transversal intersections

Yakov Varshavsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 are equal to the 'naive local terms'. To prove the result, we extend the strategy used in our previous work, where the case of contracting correspondences is treated. Our new ingredients are the observation of Verdier that specialization of an étale sheaf to the normal cone is monodromic and the assertion that local terms are 'constant in families'. As an application, we get a generalization of the Deligne-Lusztig trace formula.

Original languageAmerican English
Pages (from-to)985-1004
Number of pages20
JournalCompositio Mathematica
Volume159
Issue number5
DOIs
StatePublished - 20 May 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence.

Keywords

  • Lefschetz trace formula
  • deformation to the normal cone
  • local terms
  • Étale cohomology

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