Zero Cycles of Degree One on Principal Homogeneous Spaces

2010/09/23 by Jodi Black, Black, Jodi
Mathematics · #11E57 #11E72 #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #math.GR #math.NT #msc:11E57 #msc:11E72

paper · pdf · doi:10.48550/arxiv.1009.4621

arxiv created 2010/09/23 · arxiv updated 2010/09/24

Abstract

Let k be a field of characteristic different from 2. Let G be a simply connected or adjoint semisimple algebraic k-group which does not contain a simple factor of type E₈ and such that every exceptional simple factor of type other than G₂ is quasisplit. We show that if a principal homogeneous space under G over k admits a zero cycle of degree 1 then it has a k-rational point.

Related

• Implications of the Hasse Principle for Zero Cycles of Degree One on Principal Homogeneous Spaces
• Zero cycles on homogeneous varieties
• Very special algebraic groups
• Rationality of cycles on function field of exceptional projective homogeneous varieties
• Lois de réciprocité supérieures et points rationnels