Universal deformation rings and dihedral 2-groups

• Autores: Frauke M. Bleher
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 79, Nº 1, 2009, págs. 225-237
• Idioma: inglés
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• Resumen

  • 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.