Lectures on Applied $\ell$-adic Cohomology
Etienne Fouvry, Emmanuel Kowalski, Philippe Michel, Will Sawin

TL;DR
This paper discusses how advanced $ ext{ extlbrackdbl} ext{ extrbrackdbl}$-adic cohomology techniques, developed by Grothendieck, Deligne, Katz, and Laumon, can address classical problems in analytic number theory.
Contribution
It systematically applies deep $ ext{ extlbrackdbl} ext{ extrbrackdbl}$-adic cohomology methods to make progress on longstanding questions in analytic number theory.
Findings
Demonstrates new applications of $ ext{ extlbrackdbl} ext{ extrbrackdbl}$-adic cohomology in number theory
Provides insights into classical problems using modern cohomological techniques
Extends previous theoretical frameworks in $ ext{ extlbrackdbl} ext{ extrbrackdbl}$-adic cohomology
Abstract
We describe how a systematic use the deep methods from -adic cohomology pioneered by Grothendieck and Deligne and further developed by Katz, Laumon allow to make progress on various classical questions from analytic number theory. This text is an extended version of a series of lectures given by the third and fourth authors during the 2016 Arizona Winter School.
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