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Main Authors: Gaitsgory, Dennis, Varshavsky, Yakov
Format: Preprint
Published: 2020
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Online Access:https://arxiv.org/abs/2012.14257
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author Gaitsgory, Dennis
Varshavsky, Yakov
author_facet Gaitsgory, Dennis
Varshavsky, Yakov
contents In this paper we introduce the categorical "true local terms" maps for Artin stacks and show that they are additive and commute with proper pushforwards, smooth pullbacks and specializations. In particular, we generalizing results of [Va2] to this setting. As an application, we supply proofs of two theorems stated in [AGKRRV]. Namely, we show that the "true local terms" of the Frobenius endomorphism coincide with the "naive local terms" and that the "naive local terms" commute with !-pushforwards. The latter result is a categorical version of the classical Grothendieck--Lefschetz trace formula.
format Preprint
id arxiv_https___arxiv_org_abs_2012_14257
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Local terms for the categorical trace
Gaitsgory, Dennis
Varshavsky, Yakov
Algebraic Geometry
In this paper we introduce the categorical "true local terms" maps for Artin stacks and show that they are additive and commute with proper pushforwards, smooth pullbacks and specializations. In particular, we generalizing results of [Va2] to this setting. As an application, we supply proofs of two theorems stated in [AGKRRV]. Namely, we show that the "true local terms" of the Frobenius endomorphism coincide with the "naive local terms" and that the "naive local terms" commute with !-pushforwards. The latter result is a categorical version of the classical Grothendieck--Lefschetz trace formula.
title Local terms for the categorical trace
topic Algebraic Geometry
url https://arxiv.org/abs/2012.14257