论文标题
售价和正式的亚伯利亚集团计划在$ p $ - 极性戒指上
Affine and formal abelian group schemes on $p$-polar rings
论文作者
论文摘要
我们表明，$ p $ typical的共同亮点向量的函数在理想的字段$ k $上的特征性$ p $上定义，实际上仅取决于比$ k $ - 代数的结构较弱的结构。我们将此结构称为$ P $ -Polar $ K $ -Algebra。通过扩展，在任何$ p $ ad的仿射型组方案以及任何正式组的函数上都定义了，并且仅取决于$ p $ polar的结构。就阿贝里安·霍夫夫（Abelian Hopf）代数而言，我们表明可以在任何$ p $ -polar $ k $ -k $ -k $ -algebra $ p $上定义一个无COFFOF的HOPF代数，并且它与Compove nof $ k $ k $ -algebra $ a $ p $ p $ a $ p $ a $ a a $ a a $ a a $ a a $ p $ a-p $ a-p $ a-p a $ a a $ p $ a-p $ a-porla是-pola;双重结果可在有限的$ k $ -coalgebras上免费提供交换性HOPF代数。
We show that the functor of $p$-typical co-Witt vectors on commutative algebras over a perfect field $k$ of characteristic $p$ is defined on, and in fact only depends on, a weaker structure than that of a $k$-algebra. We call this structure a $p$-polar $k$-algebra. By extension, the functors of points for any $p$-adic affine commutative group scheme and for any formal group are defined on, and only depend on, $p$-polar structures. In terms of abelian Hopf algebras, we show that a cofree cocommutative Hopf algebra can be defined on any $p$-polar $k$-algebra $P$, and it agrees with the cofree commutative Hopf algebra on a commutative $k$-algebra $A$ if $P$ is the $p$-polar algebra underlying $A$; a dual result holds for free commutative Hopf algebras on finite $k$-coalgebras.
