Rank one case of Dwork's conjecture, by Daqing Wan

This paper proves the general rank one case of Dwork's conjecture over the affine space. It generalizes and improves the method of the preprint 141 "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 Gouvea-Mazur conjecture direction) for the unit root zeta function is obtained. The paper is to appear in JAMS.

Daqing Wan <dwan@math.uci.edu>