QUANTITATIVE SHEAF THEORY

Will Sawin; A. Forey; J. Fresán; E. Kowalski

doi:10.1090/jams/1008

QUANTITATIVE SHEAF THEORY

Will Sawin, A. Forey, J. Fresán, E. Kowalski

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We introduce a notion of complexity of a complex of ℓ-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.

Original language	English (US)
Pages (from-to)	653-726
Number of pages	74
Journal	Journal of the American Mathematical Society
Volume	36
Issue number	3
DOIs	https://doi.org/10.1090/jams/1008
State	Published - 2023
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/jams/1008

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AB - We introduce a notion of complexity of a complex of ℓ-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.

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JF - Journal of the American Mathematical Society

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QUANTITATIVE SHEAF THEORY

Abstract

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