A trace formula for F-crystals (Q793802)

Let X be a smooth and proper curve over the finite field k, and let E be an F-crystal on X. In this paper the method of \textit{P. Monsky} [Ann. Math., II. Ser. 93, 315-343 (1971; Zbl 0213.475)] is adapted to prove a Lefschetz formula for the trace of F acting on the crystalline cohomology \(H^*(X/W,E)\), where W is the ring of Witt vectors of k, provided that char(k)\(\neq 2\). There is also discussion of a wider class of systems of coefficients for which the result is valid; namely, ''F-crystals with logarithmic singularities'', in which the underlying differential equation of E (on a smooth lifting of X to W) is permitted to have regular singular points.