Resumen de Universal deformation rings and dihedral 2-groups

Frauke M. Bleher

• Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose that D is a dihedral 2-group. We prove that the universal deformation ring R(D, V) of an endo-trivial kD-module V is always isomorphic to W [/2x/2]. As a consequence, we obtain a similar result for modules V with stable endomorphism ring k belonging to an arbitrary nilpotent block with defect group D. This confirms, for such V, conjectures on the ring structure of the universal deformation ring of V that had previously been shown for V belonging to cyclic blocks or to blocks with Klein four defect groups.