Journal of the American Mathematical Society

Author(s): Daqing Wan
Journal: J. Amer. Math. Soc. 13 (2000), 807-852.
MSC (2000): Primary 11G40, 11S40; Secondary 11M41, 11G25
Posted: June 6, 2000
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In this paper, we study the higher rank case of Dwork's conjecture on the

-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

-space.

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