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arXiv · 1211.3873

Computation of Framed Deformation Functors

Pietro Ploner
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Abstract

In this work we compute the universal framed deformation functor for a reducible Galois representation $ρ$ given by direct sum of 2-dimensional representations $ρ_i$ coming from p-divisible groups. We impose the local conditions of flatness in the residual characteristic prime $p$ and semistable action in a single auxiliary prime $\ell$. The main application is the case of $ρ_i$ being the representation attached to the $p$-torsion points of an elliptic curve $E_i$ over $\mathbb{Q}$ with good reduction but in $\ell$ and semistable reduction in $\ell$. This article was inspired by a series of works of Schoof about abelian varieties with bad reduction in one prime only. Our local deformation condition correspond to reduction properties of such varieties.

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Pietro Ploner. 2013-01-22. Computation of Framed Deformation Functors. https://arxiv.org/abs/1211.3873

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