分类跟踪的本地术语

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-04-02 DOI:10.1016/j.aim.2025.110223

Dennis Gaitsgory , Yakov Varshavsky

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引用次数: 0

摘要

本文引入了Artin堆栈的范畴“真局部项”映射，并证明了它们具有适当的前推、平滑回调和专门化的可加性和可交换性。特别地，我们将[14]的结果推广到这个设置。作为应用，我们给出了[1]中两个定理的证明。也就是说，我们证明了Frobenius自同态的“真局部项”与“朴素局部项”是一致的，并且“朴素局部项”与-pushforward交换。后一个结果是经典格罗滕迪克-莱夫谢茨迹公式的一个绝对版本。

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Local terms for the categorical trace

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 [14] to this setting.

As an application, we supply proofs of two theorems stated in [1]. 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.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.