TY - JOUR
AU - Bauer, Tilman
PY - 2022/02/24
Y2 - 2022/05/27
TI - Affine and formal abelian group schemes on $p$-polar rings
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 128
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-129704
UR - https://www.mscand.dk/article/view/129704
SP -
AB - <p>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.</p>
ER -