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Higher rank case of Dwork's conjecture


Author: Daqing Wan
Journal: J. Amer. Math. Soc. 13 (2000), 807-852
MSC (2000): Primary 11G40, 11S40; Secondary 11M41, 11G25
DOI: https://doi.org/10.1090/S0894-0347-00-00339-8
Published electronically: June 6, 2000
MathSciNet review: 1775738
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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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Additional Information

Daqing Wan
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Email: dwan@math.uci.edu

DOI: https://doi.org/10.1090/S0894-0347-00-00339-8
Keywords: L-functions, $p$-adic meromorphic continuation, $\sigma$-modules
Received by editor(s): October 1, 1999
Received by editor(s) in revised form: April 10, 2000
Published electronically: June 6, 2000
Additional Notes: This work was partially supported by the National Science Foundation
Dedicated: Dedicated to the memory of Bernard Dwork
Article copyright: © Copyright 2000 American Mathematical Society

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