Towards the MacLane cohomology of finite fields
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.
scientific article; zbMATH DE number 556339