Deformation rings and images of Galois representations
Let G be a connected reductive almost simple group over the Witt ring W(F) for F a finite field of characteristic p. Let R and R' be complete noetherian local W(F)-algebras with residue field F. Under a mild condition on p in relation to structural constants of G, we show the following results:...
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Article (Journal) |
| Langue: | anglais |
| Publié: |
30 April 2026
|
| In: |
Algebra & number theory
Year: 2026, Volume: 20, Numéro: 4, Pages: 697-745 |
| ISSN: | 1944-7833 |
| DOI: | 10.2140/ant.2026.20.697 |
| Accès en ligne: | Verlag, kostenfrei, Volltext: https://doi.org/10.2140/ant.2026.20.697 Verlag, kostenfrei, Volltext: https://msp.org/ant/2026/20-4/p02.xhtml 
|
| Notes sur l'auteur: | Sara Arias-de-Reyna and Gebhard Böckle |
| Résumé: | Let G be a connected reductive almost simple group over the Witt ring W(F) for F a finite field of characteristic p. Let R and R' be complete noetherian local W(F)-algebras with residue field F. Under a mild condition on p in relation to structural constants of G, we show the following results: (1) Every closed subgroup H of G(R) with full residual image G(F) is a conjugate of a group G(A) for A⊂R a closed subring that is local and has residue field F. (2) Every surjective homomorphism G(R)→G(R') is, up to conjugation, induced from a ring homomorphism R→R'. (3) The identity map on G(R) represents the universal deformation of the representation of the profinite group G(R) given by the reduction map G(R)→G(F). This generalizes results of Dorobisz, Eardley and Manoharmayum, and in addition provides an abstract classification result for closed subgroups of G(R) with residually full image. We provide an axiomatic framework to study this type of question, also for slightly more general G, and we study in the case at hand in great detail what conditions on F or on p in relation to G are necessary for the above results to hold. |
|---|---|
| Description: | Veröffentlicht: 30. April 2026 Gesehen am 31.07.2026 |
| Description matérielle: | Online Resource |
| ISSN: | 1944-7833 |
| DOI: | 10.2140/ant.2026.20.697 |