Remark on the Serre \((\text{mod }5)\)-invariant for groups of type \(E_ 8\)
type: Item
instance of: scholarly article
title: Remark on the Serre \((\text{mod }5)\)-invariant for groups of type \(E_ 8\)
zbMATH Open document ID: 0835.20059
DOI: 10.1007/BF02110564
published in: Mathematical Notes
publication date: 1996-01-24T00:00:00Z
review text: Let \(G_0\) be a linear simple algebraic group of type \(E_8\) defined and factorable over an arbitrary field \(F\) of characteristic \(\neq 2, 3, 5\), and let \(\mu_5 \subset F^s\) be a \(\text{Gal} (F^s/F)\)- module of roots of unity of power 5. (Here we denote by \(F^s\) the separable closure of the field \(F\).) For arbitrary extensions \(L\) of the field \(F\), Serre and Rost constructed mappings \(\varphi_L : H^1 (L, G_0) \to H^3 (L, \mu^{\otimes 2}_5)\) that take a unity element to a unity element and have natural functor properties. The purpose of the present paper is to describe the kernel of the mapping \(\varphi = \varphi_F\).
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 830695
zbMATH Keywords: simple algebraic group of type \(E_ 8\)
author: V. Chernousov
MaRDI profile type: Publication
cites work: Q4064209
cites work: Regular elements of semisimple algebraic groups
cites work: Q4692288
full work available at URL: https://doi.org/10.1007/bf02110564
OpenAlex ID: W1998266555
description: scientific article; zbMATH DE number 830695