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The Weil Conjectures and Topos Theory
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The Weil Conjectures are a set of conjectures governing the number of solutions to diophantine equations mod p^n. Surprisingly, a certain generating function (due to Hasse and Weil) for the number of solutions is intimately related to the geometry of the complex solutions to the same equations! Grothendieck's famed "toposes" were instrumental in the formalization and solution of these conjectures, and remain an independently interesting topic of study to this day. In this talk we explain concretely what the Weil Conjectures are, then survey how the theory of toposes was used to solve them.
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