# Problem 95

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Markov partitions for algebraic geometry examples (Ruelle).

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### Problem 95: I think that then

Problem 95: I think that then problem I discussed with Rufus referred to his very natural version of the proof of the rationality of the zeta function for Axiom A using a Markov partition.  Can one imitate this proof for the Weil zeta function of a manifold M over a finite field (with periodic points for Frobenius replacing periodic points for hyperbolic diffeo)?  I.e. can one find in a natural way a “Markov Partition” on M?