Higher rank case of Dwork’s conjecture

Wan, Daqing

doi:10.1090/S0894-0347-00-00339-8

Higher rank case of Dwork’s conjecture
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by Daqing Wan

J. Amer. Math. Soc. 13 (2000), 807-852

DOI: https://doi.org/10.1090/S0894-0347-00-00339-8

Published electronically: June 6, 2000

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Abstract:

In this paper, we study the higher rank case of Dwork’s conjecture on the $p$-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 $n$-space.

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