------------- 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 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++