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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.14257 |
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| _version_ | 1866929253194399744 |
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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 |