IMPLICATIONS OF THE HASSE PRINCIPLE FOR ZERO CYCLES OF DEGREE ONE ON PRINCIPAL HOMOGENEOUS SPACES

摘要

Let k be a perfect field of virtual cohomological dimension ≤ 2. Let G be a connected linear algebraic group over k such that G~(sc) satisfies a Hasse principle over k. Let X be a principal homogeneous space under G over k. We show that if X admits a zero cycle of degree one, then X has a k-rational point.