Rank one case of Dwork's conjecture
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Rank one case of Dwork's conjecture

Abstract

This paper proves the general rank one case of Dwork's conjecture over the affine space. It generalizes and improves the method of ANT-0141 "Dwork's conjecture on unit root zeta functions" (Ann. Math., 150(1999), 867-929). In addition, explicit information about the zeros and poles (along the Gouv\^ea-Mazur conjecture direction) for the unit root zeta function is obtained. The paper is to appear in JAMS.

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