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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Quantitative sheaf theory
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by Will Sawin, A. Forey, J. Fresán and E. Kowalski
J. Amer. Math. Soc. 36 (2023), 653-726
Published electronically: August 17, 2022


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.
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Bibliographic Information
  • Will Sawin
  • Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
  • MR Author ID: 1022068
  • Email:
  • A. Forey
  • Affiliation: EPFL/SB/TAN, Station 8, CH-1015 Lausanne, Switzerland
  • MR Author ID: 1231383
  • ORCID: 0000-0002-5999-3831
  • Email:
  • J. Fresán
  • Affiliation: CMLS, École polytechnique, F-91128 Palaiseau cedex, France
  • MR Author ID: 816893
  • ORCID: 0000-0002-8550-6646
  • Email:
  • E. Kowalski
  • Affiliation: D-MATH, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
  • MR Author ID: 250736
  • Email:
  • Received by editor(s): March 4, 2021
  • Received by editor(s) in revised form: November 22, 2021, and February 1, 2022
  • Published electronically: August 17, 2022
  • Additional Notes: The first author was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation and by NSF grant DMS-2101491. The second and fourth authors were supported by the DFG-SNF lead agency program grant 200020L_175755. The second author was supported by SNF Ambizione grant PZ00P2_193354. The third author was partially supported by the grant ANR-18-CE40-0017 of the Agence Nationale de la Recherche.
  • © Copyright 2022 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 36 (2023), 653-726
  • MSC (2020): Primary 14F20; Secondary 11T23
  • DOI:
  • MathSciNet review: 4583773