TY - JOUR

T1 - Group action on the deformations of a formal group over the ring of Witt vectors

AU - Demchenko, Oleg

AU - Gurevich, Alexander

PY - 2019

Y1 - 2019

N2 - A recent result by the authors gives an explicit construction for a universal deformation of a formal group φ of finite height over a finite field k. This provides in particular a parametrization of the set of deformations of φ over the ring 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 Autk(φ) on the set of O-deformations of φ 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.

AB - A recent result by the authors gives an explicit construction for a universal deformation of a formal group φ of finite height over a finite field k. This provides in particular a parametrization of the set of deformations of φ over the ring 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 Autk(φ) on the set of O-deformations of φ 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.

UR - http://www.scopus.com/inward/record.url?scp=85070345271&partnerID=8YFLogxK

U2 - 10.1017/nmj.2017.43

DO - 10.1017/nmj.2017.43

M3 - Article

VL - 235

SP - 42

EP - 57

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -