2016
DOI: 10.1112/s0010437x16007582
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The inverse deformation problem

Abstract: Abstract. We show the inverse deformation problem has an affirmative answer: given a complete local noetherian ring A with finite residue field k k k, we show that there is a topologically finitely generated profinite group Γ and an absolutely irreducible continuous representation ρ : Γ → GLn(k k k) such that A is the universal deformation ring for Γ, ρ.

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Cited by 3 publications
(10 citation statements)
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“…(c) Part (c) for G = SL n and for deformations of the given π but into GL n is a result due to, independently, Dorobisz and Eardly-Manoharmayum; see [Dor16,EM16]. Their results are more complete than what we state above and also include p = 2, 3.…”
Section: Introductionmentioning
confidence: 66%
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“…(c) Part (c) for G = SL n and for deformations of the given π but into GL n is a result due to, independently, Dorobisz and Eardly-Manoharmayum; see [Dor16,EM16]. Their results are more complete than what we state above and also include p = 2, 3.…”
Section: Introductionmentioning
confidence: 66%
“…For the last claim note that under (csc) we have H c R = H R by Lemma 4.3. We have the following generalization of [EM16,Dor16] from GL n to arbitrary G , under the same basic hypotheses; cf. Remark 5.6.…”
Section: Rings As Universal Deformation Ringsmentioning
confidence: 99%
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