The cohomology of Monsky and Washnitzer
摘要
The Zeta-function of an algebraic variety over a finite field can be expressed in terms of a Frobenius operator acting on p-adic cohomology groups of this variety. Those cohomology groups, based on work of B. Dwork, are called the Monsky-Washnitzer cohomology. The first four sections of this paper give a survey of the papers of Monsky and Washnitzer. Their work is simplified and slightly extended by the use af Artin-approximation and some rigid analysis. In section 5 the connection with Dwork's work is indicated, Adolphson's index theorem is given in a different form in section 6. Dwork's remarkable formula for the unit root of an elliptic curve and properties of the solutions of the hypergeometric differential equation with parameters ½, ½, 1 are proved in detail in section 7.