Wild Betti sheaves

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

10 pages, note in honour of Gerard Laumon