We show that framed deformation rings of mod p representations of the absolute Galois group of a p -adic local field are complete intersections of expected dimension. We determine their irreducible components and show that they and their special fibres are normal and complete intersection. As an application, we prove density results of loci with prescribed p -adic Hodge theoretic properties.
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Böckle et al. (2023) studied this question.
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