Hironaka's additive group scheme. II
type: Item
instance of: scholarly article
title: Hironaka's additive group scheme. II
zbMATH Open document ID: 0569.14021
author: Tadao Oda
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1983-01-01T00:00:00Z
review text: Hironaka's additive group schemes are subgroup schemes of a vector group scheme over a field k of positive characteristic p. In part I of this paper [in Number Theory, Algebr. Geom., Commut. Algebra, in Honor of Y. Akizuki, 181-219 (1973; Zbl 0287.14014)] the author showed that these group schemes had a ''linear-algebra-type'' description. In the present work, he provides an alternative description which in addition allows him to produce a versal family of Hironaka subgroup schemes. - The description, while explicit, is difficult to summarize. Briefly: let S be a polynomial ring over k, \(L_ 0\) the k-subspace of linear forms in S, K the field of all elements such that some iterated Frobenius takes them to k and \(K_ e\) whose \(p^ e\)-th power is in k. V is a subspace of \(K\otimes L_ 0\) satisfying a technical condition. Let L(B) be the sum of the \(p^ e\)-th powers of \(V\cap (K_ e\otimes L_ 0)\), let I be the ideal that it generates in S, and let \(B=Spec(S/I)\). Then B is a Hironaka subgroup scheme of the vector group Spec(S), and all such arise this way.
Mathematics Subject Classification ID: 14L15
Mathematics Subject Classification ID: 14K05
zbMATH DE Number: 3908578
zbMATH Keywords: Hironaka additive group scheme
reviewed by: Andy R. Magid
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195182025
OpenAlex ID: W2046917067
cites work: Contact maximal en caractéristique positive
cites work: Additive groups associated with points of a projective space
cites work: Hironaka’s additive group schemes
cites work: A versal family of Hironaka's additive group schemes
cites work: On Hironaka's additive groups associated with points in projective space
DOI: 10.2977/PRIMS/1195182025
description: scientific article; zbMATH DE number 3908578