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A newer version of this preprint is 0141 and so this dvi file has been removed.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 <dwan@math.uci.edu>