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Dec 23, 2009 at 5:45 comment added shenghao two comments: (1) for compact supp cohomology, the absolute values of eigenvalues are LESS than.... (2) for proper varieties with quotient singularities, we still have functional equation and RH, because they are coarse moduli spaces of proper smooth DM stacks, for which H^i is pure of weight i.
Nov 25, 2009 at 8:30 comment added Ben Webster I believe rationality still holds. This should just be looking at action of the Frobenius on c.s. Cohomology. The statement on eigenvalues is that they're always bigger than the Riemann hypothesis would lead you to guess (but I think are still algebraic integers).
Nov 24, 2009 at 15:53 comment added David E Speyer A comment and a question: (1) It is still true that the zeta function is rational. (2) I always get confused about what can be said about the eigenvalues of Frobenius acting on compactly supported H^i(X) for X smooth but not projective. What's the right statement?
Nov 24, 2009 at 15:46 vote accept John McCarthy
Nov 25, 2009 at 18:21
Nov 24, 2009 at 15:37 history answered Ben Webster CC BY-SA 2.5