经典代数群的上同调
Cohomology of classical algebraic groups from the functorial viewpoint
摘要：
证明了严格多项式函子范畴中的扩张群计算经典代数群的有理上同调。这个结果以前只知道对一般线性群。我们给出了经典代数群研究中的几个应用，如上同调稳定性，外上积的内射性，以及系数在霍普夫代数中的经典代数群的（稳定）上同调上的霍普夫代数结构的存在性.我们的结果也开辟了新的显式上同调计算的方式。我们给出了一个例子的启发，最近的计算Djament和Vespa。
英文摘要：
We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study of classical algebraic groups, such as a cohomological stabilization property, the injectivity of external cup products, and the existence of Hopf algebra structures on the (stable) cohomology of a classical algebraic group with coefficients in a Hopf algebra. Our result also opens the way to new explicit cohomology computations. We give an example inspired by recent computations of Djament and Vespa.
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