论文标题
azumaya代数和方案上的二次对障碍物
Azumaya Algebras and Obstructions to Quadratic Pairs over a Scheme
论文作者
论文摘要
我们研究了Azumaya代数的二次对，其基础方案S与Caln {è} S和Fasel所定义的基本方案S相关，从而在中央简单代数上概括了二次对的案例（KNUS，Merkurjev，Merkurjev，Rost，Rost，Tignol）。我们描述了与s相结合的Azumaya代数的共同体障碍物，以接收二次对。当s仿射时，这种阻塞会消失，但是通常并非平凡。特别是，我们构建了具有非平凡障碍的明确例子。
We investigate quadratic pairs for Azumaya algebras with involutions over a base scheme S as defined by Calm{è}s and Fasel, generalizing the case of quadratic pairs on central simple algebras over a field (Knus, Merkurjev, Rost, Tignol). We describe a cohomological obstruction for an Azumaya algebra over S with orthogonal involution to admit a quadratic pair. When S is affine this obstruction vanishes, however it is non-trivial in general. In particular, we construct explicit examples with non-trivial obstructions.
