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Reductions of modular Galois representations of Slope (2,3)

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arxiv 1801.08820 v4 pith:55VQSPUF submitted 2018-01-26 math.NT

classification math.NT
keywords galoisreductionsrepresentationsslopeabsolutearbitrarybhattacharya-ghatebuilding
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abstract

We compute the semisimplifications of the mod-$p$ reductions of $2$-dimensional crystalline representations of the absolute Galois group of the p-adic numbers of slope $(2,3)$ and arbitrary weight, building on work of Bhattacharya-Ghate

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  1. Reductions of some two-dimensional crystalline representations via Kisin modules

    math.NT 2019-08 accept novelty 7.0 of 10

    For v_p(a_p) > floor((k-1)/p), the semisimple mod p reduction of the crystalline representation V_{k,a_p} is V_{k,0}.

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