Dwork's conjecture on unit root zeta functions, by Daqing Wan
A newer version of this preprint is 0141 and so this dvi file has been
removed. In this article, we introduce a systematic new method to study the conjectural
p-adic meromorphic continuation of Dwork's unit root zeta function attached to
an ordinary family of algebraic varieties defined over a finite field. This
method can be used to prove Dwork's conjecture in the rank one case. It can
also be used to extend and prove a weak version of Gouvea-Mazur's conjecture
from the ordinary family of elliptic curves (modular forms) to an ordinary
family of algebraic varieties with one p-adic unit root fibre by fibre.
We shall introduce another method in a future article which combined with
the method of the present paper will be able to prove Dwork's conjecture
in higher rank case as well.
Daqing Wan <firstname.lastname@example.org>