论文标题
蜂窝$ \ mathbb a^1 $ - 知识和Matsumoto定理的动机版本
Cellular $\mathbb A^1$-homology and the motivic version of Matsumoto's theorem
论文作者
论文摘要
我们为$ \ mathbb a^1 $的新版本定义了一种称为蜂窝$ \ mathbb a^1 $ - 知理的知识，用于在一个领域的平滑方案，该领域承认，通过共同体学上的开放式化机构越来越多地过滤过过滤，并具有共同体学上微不足道的封闭阶层。我们提供了几项细胞$ \ mathbb a^1 $的明确计算，并使用它们来确定在任意领域的分裂还原组的$ \ m artbb a^1 $ - fundaundaMental group，从而获得了Matsumoto的动机版本的动机版本，该版本是对分裂的，简单地连接Alge Alge Algebraic connected Algebraic of Split，Split splaine Central interions of Split spline Central interions。 As applications, we uniformly explain and generalize results due to Brylinski-Deligne and Esnault-Kahn-Levine-Viehweg, determine the isomorphism classes of central extensions of such an algebraic group by an arbitrary strictly $\mathbb A^1$-invariant sheaf and also reprove classical results of E. Cartan on homotopy groups of complex Lie groups.
We define a new version of $\mathbb A^1$-homology, called cellular $\mathbb A^1$-homology, for smooth schemes over a field that admit an increasing filtration by open subschemes with cohomologically trivial closed strata. We provide several explicit computations of cellular $\mathbb A^1$-homology and use them to determine the $\mathbb A^1$-fundamental group of a split reductive group over an arbitrary field, thereby obtaining the motivic version of Matsumoto's theorem on universal central extensions of split, semisimple, simply connected algebraic groups. As applications, we uniformly explain and generalize results due to Brylinski-Deligne and Esnault-Kahn-Levine-Viehweg, determine the isomorphism classes of central extensions of such an algebraic group by an arbitrary strictly $\mathbb A^1$-invariant sheaf and also reprove classical results of E. Cartan on homotopy groups of complex Lie groups.
