The multiplicative group over Sigma maps to the prismatization of the multiplicative group over Spf

A 1-dimensional formal group over the prismatization of Spf Z_p

Let Sigma denote the prismatization of Spf (Z_p). The multiplicative group
over Sigma maps to the prismatization of the multiplicative group over Spf
(Z_p). We prove that the kernel of this map is the Cartier dual of some
1-dimensional formal group over Sigma. We obtain some results about this formal
group (e.g., we describe its Lie algebra). We give a very explicit description
of the pullback of the formal group to the quotient of the q-de Rham prism by
the action of the multiplicative group of Z_p.