Higher rank case of Dwork’s conjecture
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Higher rank case of Dwork’s conjecture


In this paper, we study the higher rank case of Dwork’s conjecture on the p p -adic meromorphic continuation of the pure slope L-functions arising from the slope decomposition of an overconvergent F-crystal. Our main result is to reduce the general case of the conjecture to the special case when the pure slope part has rank one and when the base space is the simplest affine n n -space.

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