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arXiv · 1411.3759

Finiteness of unramified deformation rings

Patrick B. Allen·Frank Calegari
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Abstract

We prove that the universal unramified deformation ring $R^{\mathrm{unr}}$ of a continuous Galois representation $\overlineρ: G_{F^{+}} \rightarrow \mathrm{GL}_n(k)$ (for a totally real field $F^{+}$ and finite field $k$) is finite over $\mathcal{O} = W(k)$ in many cases. We also prove (under similar hypotheses) that the universal deformation ring $R^{\mathrm{univ}}$ is finite over the local deformation ring $R^{\mathrm{loc}}$.

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Patrick B. Allen, Frank Calegari. 2014-11-13. Finiteness of unramified deformation rings. https://doi.org/10.2140/ant.2014.8.2263

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