Author:
DEMCHENKO OLEG,GUREVICH ALEXANDER
Abstract
A recent result by the authors gives an explicit construction for a universal deformation of a formal group
$\unicode[STIX]{x1D6F7}$
of finite height over a finite field
$k$
. This provides in particular a parametrization of the set of deformations of
$\unicode[STIX]{x1D6F7}$
over the ring
${\mathcal{O}}$
of Witt vectors over
$k$
. Another parametrization of the same set can be obtained through the Dieudonné theory. We find an explicit relation between these parameterizations. As a consequence, we obtain an explicit expression for the action of
$\text{Aut}_{k}(\unicode[STIX]{x1D6F7})$
on the set of
${\mathcal{O}}$
-deformations of
$\unicode[STIX]{x1D6F7}$
in the coordinate system defined by the universal deformation. This generalizes a formula of Gross and Hopkins and the authors’ result for one-dimensional formal groups.
Publisher
Cambridge University Press (CUP)