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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish (US)
Pages (from-to)653-726
Number of pages74
JournalJournal of the American Mathematical Society
Issue number3
StatePublished - 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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