论文标题
动机的同伴学和无限群体计划
Motivic cohomology and infinitesimal group schemes
论文作者
论文摘要
对于$ k $，一个特征性的$ p> 0 $和$ g/k $的完美领域，$ g的$ p $ a nonttorsion prime for $ g，我们计算几何$ p $ p $ p $ p $ p $ p $ bg $ bg _ {（r）} $ $ g _ {（r）$ r $ r $ r p p r b r bg r b r bf ious yius yius yius yius yius yius yous yous yous yous yous yous yous yius由于奎师那而引起的Eilenberg-Moore光谱序列。 对于有限类型的平坦仿射组方案$ g/k $，我们定义了一个周期类图，从mod $ p $ p $动机共同体中分类的空间$ bg $ to mod $ p $ p $ p $ p $ p $étale的动机共同体，分类stack $ \ \ \ \ m nathcal {b}g。班级地图以获取一些示例，包括Frobenius内核。
For $k$ a perfect field of characteristic $p>0$ and $G/k$ a split reductive group with $p$ a non-torsion prime for $G,$ we compute the mod $p$ motivic cohomology of the geometric classifying space $BG_{(r)}$, where $G_{(r)}$ is the $r$th Frobenius kernel of $G.$ Our main tool is a motivic version of the Eilenberg-Moore spectral sequence, due to Krishna. For a flat affine group scheme $G/k$ of finite type, we define a cycle class map from the mod $p$ motivic cohomology of the classifying space $BG$ to the mod $p$ étale motivic cohomology of the classifying stack $\mathcal{B}G.$ This also gives a cycle class map into the Hodge cohomology of $\mathcal{B}G.$ We study the cycle class map for some examples, including Frobenius kernels.
