论文标题
圆环对特征零字段的仿射品种的作用
Torus actions on affine varieties over characteristic zero fields
论文作者
论文摘要
使用GALOIS血统工具，我们将正常仿射代数品种的Altmann-Hausen呈现扩展到在特征零的代数闭合场上具有有效的圆环作用，以使地面场是特征零的任意场。在这种情况下，表演圆环可能具有非平凡的扭转，我们需要其他数据来编码此类品种。最后，我们专注于具有二维圆环动作的仿射品种，并提供了一种确定托索尔何时微不足道的方法，在这种情况下，Altmann-Hausen介绍简化了。
Using Galois descent tools, we extend the Altmann-Hausen presentation of normal affine algebraic varieties endowed with an effective torus action over an algebraically closed field of characteristic zero to the case where the ground field is an arbitrary field of characteristic zero. In this context, the acting torus may have non-trivial torsors and we need additional data to encode such varieties. Finally, we focus on affine varieties endowed with a two-dimensional torus action and we provide a method for determining when a torsor is trivial, in which case the Altmann-Hausen presentation simplifies.
