The Hrushovski-Lang-Weil estimates

K. V. Shuddhodan*, Yakov Varshavsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this work, we give an algebro-geometric proof of Hrushovski's generalization of the Lang-Weil estimates on the number of points in the intersection of a correspondence with the graph of the Frobenius map. This result has numerous applications to various areas of mathematics, including model theory, algebraic dynamics, group theory and arithmetic algebraic geometry.

Original languageAmerican English
Pages (from-to)651-687
Number of pages37
JournalAlgebraic Geometry
Issue number6
StatePublished - Nov 2022

Bibliographical note

Publisher Copyright:
© Foundation Compositio Mathematica 2022. This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited. For commercial re-use, please contact the Foundation Compositio Mathematica.


  • Cohomological methods.
  • Finite fields
  • Intersection theory


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