------------- I have not really understood the role of toposes in Grothendieck and Deligne's work on the Weil conjectures. Is it roughly right to say: For etale cohomology over a field k you put the etale topology on the category of (finitely presented?) k-algebras and look at the corresponding topos. Schemes over k are objects in that topos, and the etale cohomology of a scheme S is the topos cohomology of the slice of that topos over S. Or is that hopelessly wrong? Colin McLarty +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
What you are saying is definitely right except for the fact that you should consider not the category of k-algebras but the opposite category of affine schemes over k with etale (or whatever else) topology. Vladimir Voevodsky. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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