Quantitative sheaf theory
Abstract
We introduce a notion of complexity of a complex of ell-adic sheaves on a quasi-projective variety and prove that the six operations are "continuous", in the sense that the complexity of the output sheaves is bounded solely in terms of the complexity of the input sheaves. A key feature of complexity is that it provides bounds for the sum of Betti numbers that, in many interesting cases, can be made uniform in the characteristic of the base field. As an illustration, we discuss a few simple applications to horizontal equidistribution results for exponential sums over finite fields.
Keywords
Cite
@article{arxiv.2101.00635,
title = {Quantitative sheaf theory},
author = {W. Sawin and A. Forey and J. Fresán and E. Kowalski},
journal= {arXiv preprint arXiv:2101.00635},
year = {2022}
}
Comments
v4, 69 pages; the key ideas of this paper are due to W. Sawin; A. Forey, J. Fres\'an and E. Kowalski drafted the current version of the text; final version to appear in JAMS