\(L\) functions associated to overconvergent \(F\)-isocrystals. II: Unit roots and poles
[For part I of this paper see Math. Ann., 296, No. 3, 557-576 (1993; Zbl 0789.14015).] It is given a construction of the Artin-Schreier exact sequence on the syntomic site of a scheme, not necessarily smooth and proper. Under the last conditions the construction was done by \textit{J. M. Fontaine} and \textit{W. Messing} [in: Current trends in arithmetical algebraic geometry, Proc. Summer Res. Conf., Arcata 1985, Contemp. Math. 67, 179-207 (1987; Zbl 0632.14016)]. N. Katz has conjectured that \(p\)-adic unit roots and poles of the \(L\)-functions associated to a representation of the fundamental group of a variety over \(\mathbb{F}_q\) can be expressed in terms of \(p\)-adic étale cohomologies. The authors prove this conjecture as well as many interesting corollaries.
scientific article; zbMATH DE number 1026493