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Hilbert-Samuel multiplicities of certain deformation rings

Fabian Sander

Number 6
Author Fabian Sander
Year 2014

We compute presentations of crystalline framed deformation rings of a two dimensional representation ρ¯ of the absolute Galois group of Qp, when ρ¯ has scalar semi-simplification, the Hodge-Tate weights are small and p>2. In the non-trivial cases, we show that the special fibre is geometrically irreducible, generically reduced and the Hilbert-Samuel multiplicity is either 1, 2 or 4 depending on ρ¯. We show that in the last two cases the deformation ring is not Cohen-Macaulay.

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