论文标题
可分离的代数和Coflasque决议
Separable algebras and coflasque resolutions
论文作者
论文摘要
在非关闭场上，使用可分离代数作为不变的策略来区分代数和几何对象。最著名的例子是Severi-Brauer品种与中央简单代数之间的深厚联系。对于更一般的品种，可以使用线束的内态代数，不可分解的向量束或其派生类别中的特殊对象的代数。 我们使用Galois的共同体来描述一个新的还原代数群体的新不变，该群体准确地捕获了这种策略失败的情况。我们的主要结果是根据Colliot-Thélène引入的线性代数群的Coflasque分辨率而不变的。我们确定这种不变是否对于许多领域来说都是微不足道的。对于数字字段，我们表明它与线性代数组的Tate-Shafarevich组一致，直到在真实的地方进行行为。
Over a non-closed field, it is a common strategy to use separable algebras as invariants to distinguish algebraic and geometric objects. The most famous example is the deep connection between Severi-Brauer varieties and central simple algebras. For more general varieties, one might use endomorphism algebras of line bundles, of indecomposable vector bundles, or of exceptional objects in their derived categories. Using Galois cohomology, we describe a new invariant of reductive algebraic groups that captures precisely when this strategy will fail. Our main result characterizes this invariant in terms of coflasque resolutions of linear algebraic groups introduced by Colliot-Thélène. We determine whether or not this invariant is trivial for many fields. For number fields, we show it agrees with the Tate-Shafarevich group of the linear algebraic group, up to behavior at real places.
