1. Introduction Let G be an algebraic group over a field F, V a generically free representation of G (i.e., the stabilizer of the generic point in V is trivial) and U C V a Gequivariant open subset such that there is a G-torsor f : U → U/G. This is a versal G-torsor, in particular, every G-torsor over a field extension K/F with K infinite is isomorphic to the fiber of f over a K-point of U/G. Thus, the K-points of U/G parameterize all G-torsors over Spec(K).
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机译：1.引言令我们将G成为领域F的代数组，V的G（即，V中的通用点的稳定器是琐碎的透视的稳定器）和UCV A Gequivariant的开放子集，使得存在G-Torsor F. ：U→U / g。 这是具有V-rorsor的变化，特别是具有K无限的场延伸k / f上的每个g-纹体对U / g的k点上的F的纤维同构。 因此，U / G的k点参数通过规范（k）参数化所有G扭转器。
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