arXiv subjects
Publications and source records attributed to Fabian Sander.
We give a new local proof of the Breuil-Mézard conjecture in the case of a reducible representation of the absolute Galois group of $\mathbb{Q}_p$, $p>2$, that has scalar semi-simplification, via a formalism of Paškūnas.
We compute presentations of crystalline framed deformation rings of a two dimensional representation $\barρ$ of the absolute Galois group of $\mathbb{Q}_p$, when $\barρ$ 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 $\barρ$. We show that in the last two cases the deformation ring is not Cohen-Macaulay.