p-adic Hodge-theoretic properties of \'etale cohomology with mod p coefficients, and the cohomology of Shimura varieties
p-adic Hodge-theoretic properties of \'etale cohomology with mod p coefficients, and the cohomology of Shimura varieties
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具有 mod p 系数的 etale 上同调的 p 进 Hodge 理论性质，以及 Shimura 簇的上同调
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发表时间：
2012
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通讯作者：
Toby Gee
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作者：
M. Emerton;Toby Gee
我们表明，在\(Q_p\)的有限扩张\(K\)上具有半稳定约化的光滑射影簇的模\(p\)上同调，嵌入到具有在预期范围内的霍奇 - 塔特权的半稳定伽罗瓦表示的模\(p\)约化中（至少在半单化之后，在上同调度数\(>1\)的情况下）。我们证明了带有下降数据的精细化结果，并将这些结果应用于酉志村簇的上同调，推导出消失结果以及对塞尔猜想的权部分的应用。
We show that the mod p cohomology of a smooth projective variety with semistable reduction over K, a finite extension of Qp, embeds into the reduction modulo p of a semistable Galois representation with Hodge-Tate weights in the expected range (at least after semisimplifying, in the case of the cohomological degree > 1). We prove refinements with descent data, and we apply these results to the cohomology of unitary Shimura varieties, deducing vanishing results and applications to the weight part of Serre's conjecture.