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weil-conjectures
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Weil saw that counting points on varieties over finite fields should behave like topology. Grothendieck built étale cohomology to make that literal, and Deligne used it to prove the hardest part. This is the finite-field shadow of the Riemann hypothesis, and the reason many believe the original is true.
Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.
Posed 1949, André Weil. Closed 1974, Pierre Deligne (the Riemann hypothesis part).