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arXiv · 2103.00106

Ordinarity of Local Galois Representation Arising from Dwork Motives

Lie Qian
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Abstract

In this paper, we prove that for suitably chosen Dwork motives, the local Galois representation arising from middle cohomology of fibers over a point with $p$-adic valuation $<0$ on the base is regular and ordinary. The result will be crucial in the forthcoming work Potential Automorphy for $GL_n$. The proof consists of the construction of a semistable blowup and a use of Hyodo-Kato's log crystalline cohomology theory.

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Lie Qian. 2021-02-27. Ordinarity of Local Galois Representation Arising from Dwork Motives. https://arxiv.org/abs/2103.00106

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