Towards the MacLane cohomology of finite fields
type: Item
instance of: scholarly article
title: Towards the MacLane cohomology of finite fields
zbMATH Open document ID: 0798.18009
DOI: 10.1007/BF01231771
author: Vincent Franjou
author: Jean Lannes
author: Lionel Schwartz
published in: Inventiones Mathematicae
publication date: 1994-10-31T00:00:00Z
full work available at URL: https://eudml.org/doc/144180
review text: This paper describes a new method to compute the MacLane cohomology of finite fields. The present theory is closely related to \textit{L. Breen}'s ``extensions du groupe additif'' [Inst. Haut. Étud. Sci., Publ. Math. 48, 39-125 (1978; Zbl 0404.14018)] and \textit{M. Bökstedt}'s topological Hochschild homology [work to appear; see also \textit{T. Pirashvili} and \textit{F. Waldhausen}, MacLane homology and topological Hochschild homology, J. Pure Appl. Algebra 82, No. 1, 81-98 (1992; Zbl 0767.55010)], and hence to stable \(K\)-theory. The main tool is a cancellation theorem for MacLane cohomology of the field \(\mathbb{F}_ p\) with coefficients in the symmetric algebra where the Frobenius endomorphism is inverted. Then comes the analysis of the Koszul and the De Rham complexes in non-zero characteristic.
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 55N15
zbMATH DE Number: 556339
zbMATH Keywords: MacLane cohomology
zbMATH Keywords: finite fields
zbMATH Keywords: topological Hochschild homology
zbMATH Keywords: Frobenius endomorphism
reviewed by: Georges Hoff
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 556339