On duality over a certain divided power algebra with positive characteristic
type: Item
instance of: scholarly article
title: On duality over a certain divided power algebra with positive characteristic
zbMATH Open document ID: 0893.12006
DOI: 10.1007/BF02678187
author: Takakazu Satoh
published in: Manuscripta Mathematica
publication date: 1998-08-24T00:00:00Z
full work available at URL: https://eudml.org/doc/156258
review text: Let \(R\) be a commutative overring of the algebraic closure of the Galois field \(GF(q)\), complete with respect to a non-archimedean dense absolute value. Starting from a normed \(R\)-module \(M\) with a finite orthonormal basis, the author builds the algebra \(\text{Sym} M= \oplus \text{Sym}^nM\) and studies non-archimedean analysis on its graded dual \(A'\). The study is motivated by the Carlitz zeta function \(\zeta_A(s)\) of \(A=GF(q)[T]\) defined as the sum \(\sum_{n\in A} {1\over n^s}\) \((n\) monic) with values in the field \(GF(q) ((T^{-1}))\) of the formal Laurent series over \(GF(q)\).
Mathematics Subject Classification ID: 12J25
Mathematics Subject Classification ID: 11G09
zbMATH DE Number: 1019706
zbMATH Keywords: duality
zbMATH Keywords: divided power algebra
zbMATH Keywords: non-archimedean valued fields
zbMATH Keywords: Carlitz zeta function
reviewed by: Witold Więsław
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1019706