Affine and formal abelian group schemes on p-polar rings

Authors

  • Tilman Bauer

DOI:

https://doi.org/10.7146/math.scand.a-129704

Abstract

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.

References

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Published

2022-02-24

How to Cite

Bauer, T. (2022). Affine and formal abelian group schemes on p-polar rings. MATHEMATICA SCANDINAVICA, 128(1). https://doi.org/10.7146/math.scand.a-129704

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Section

Articles