Tsukuba Journal of Mathematics

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

Go Yamashita

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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


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