A construction of tame sheaves and tame de Rham--Witt cohomology
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914582281322496 |
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| author | Merici, Alberto Rülling, Kay Saito, Shuji |
| author_facet | Merici, Alberto Rülling, Kay Saito, Shuji |
| contents | In this article, we consider an algebraic version of the tame site of a pair $(X,\widetilde{X})$. With this definition, we provide a general machinery to construct a tame sheaf from the data of an étale sheaf on $X$ and a family of local tame sections. We apply this construction to the big de Rham--Witt sheaves with tame sections defined by log poles and, over a field, to reciprocity sheaves, and deduce some consequences. As an application, we compare tame syntomic cohomology with the Nygaard filtration on the tame de Rham--Witt complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20858 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A construction of tame sheaves and tame de Rham--Witt cohomology Merici, Alberto Rülling, Kay Saito, Shuji Algebraic Geometry 14F30, 14F06, 13F35 In this article, we consider an algebraic version of the tame site of a pair $(X,\widetilde{X})$. With this definition, we provide a general machinery to construct a tame sheaf from the data of an étale sheaf on $X$ and a family of local tame sections. We apply this construction to the big de Rham--Witt sheaves with tame sections defined by log poles and, over a field, to reciprocity sheaves, and deduce some consequences. As an application, we compare tame syntomic cohomology with the Nygaard filtration on the tame de Rham--Witt complex. |
| title | A construction of tame sheaves and tame de Rham--Witt cohomology |
| topic | Algebraic Geometry 14F30, 14F06, 13F35 |
| url | https://arxiv.org/abs/2605.20858 |