I think of the Weight Monodromy conjecture as an analogue of the Weil conjectures in the case of bad reduction. The Weil conjectures of course have lots of applications, from point counting to bounding exponential sums and a lot more.
What are some consequences of the Weight monodromy conjecture (either in the cases where it has already been proven or in conjectural cases). Does it imply any other open conjectures, for instance?
