We show that the functor of $p$-typical co-Witt vectors on commutative algebras over a perfect field $k$ characteristic $p$ is defined on, and in fact only depends weaker structure than $k$-algebra. call this $p$-polar By extension, functors points for any $p$-adic affine group scheme formal are depend structures. In terms abelian Hopf algebras, we cofree cocommutative algebra can be $k$-algebr...

Abstract The Fourier algebra of the affine group real line has a natural identification, as Banach space, with space trace-class operators on $$L^2({{\mathbb {R}}}^\times , dt/ |t|)$$ L 2 ( R × ,</mml...