A small remark on the filtered $\varphi$-module of Fermat varieties and Stickelberger's theorem

Abstract

We show that the weakly admissibility of the filtered $\varphi$-module with coefficients of Fermat varieties in the sense of Fontaine essentially expresses Stickelberger's theorem in Iwasawa theory. In particular, it gives us a simple re-proof of the weakly admissibility of it.