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Quantitative sheaf theory

Authors :
Sawin, W.
Forey, A.
Fresán, J.
Kowalski, E.
Publication Year :
2021

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.<br />Comment: 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

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2101.00635
Document Type :
Working Paper