Wild Betti sheaves

Peter Scholze

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arXiv · 2505.24599

Wild Betti sheaves

Peter Scholze

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Abstract

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 $\mathrm{Spec}(\mathbb Z)$.

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Peter Scholze. 2025-05-30. Wild Betti sheaves. https://arxiv.org/abs/2505.24599

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