Wild Betti sheaves
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908386135638016 |
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| author | Scholze, Peter |
| author_facet | Scholze, Peter |
| contents | In this note, we consider the problem of constructing an enlargement of the category of Betti sheaves that supports an ``exponential local system'' on $\mathbb R$, and a Fourier equivalence defined on all sheaves. We show that there is a universal solution, recovering a construction of Tamarkin known also as ``enhanced sheaves''. The universality property implies that the category of coefficients of this theory is, in a suitable sense, a nontrivial $\mathbb R_{>0}$-torsor over $\mathrm{Spec}(\mathbb Z)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wild Betti sheaves Scholze, Peter Algebraic Geometry Algebraic Topology Number Theory Symplectic Geometry 14F25, 55N30, 53D37 In this note, we consider the problem of constructing an enlargement of the category of Betti sheaves that supports an ``exponential local system'' on $\mathbb R$, and a Fourier equivalence defined on all sheaves. We show that there is a universal solution, recovering a construction of Tamarkin known also as ``enhanced sheaves''. The universality property implies that the category of coefficients of this theory is, in a suitable sense, a nontrivial $\mathbb R_{>0}$-torsor over $\mathrm{Spec}(\mathbb Z)$. |
| title | Wild Betti sheaves |
| topic | Algebraic Geometry Algebraic Topology Number Theory Symplectic Geometry 14F25, 55N30, 53D37 |
| url | https://arxiv.org/abs/2505.24599 |