## Tsukuba Journal of Mathematics

- Tsukuba J. Math.
- Volume 40, Number 1 (2016), 119-124.

### 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.

#### Article information

**Source**

Tsukuba J. Math., Volume 40, Number 1 (2016), 119-124.

**Dates**

Received: 15 January 2016

Revised: 13 May 2016

First available in Project Euclid: 24 September 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.tkbjm/1474747490

**Digital Object Identifier**

doi:10.21099/tkbjm/1474747490

**Mathematical Reviews number (MathSciNet)**

MR3550935

**Zentralblatt MATH identifier**

06642044

**Subjects**

Primary: 11D41: Higher degree equations; Fermat's equation

Secondary: 11R23: Iwasawa theory 14F30: $p$-adic cohomology, crystalline cohomology

**Keywords**

Fermat varieties Stickelberger's theorem filtered $\varphi$-modules Newton polygon Hodge polygon crystalline cohomology Jacobi sum Gauss sum

#### Citation

Yamashita, Go. A small remark on the filtered $\varphi$-module of Fermat varieties and Stickelberger's theorem. Tsukuba J. Math. 40 (2016), no. 1, 119--124. doi:10.21099/tkbjm/1474747490. https://projecteuclid.org/euclid.tkbjm/1474747490