Integral $p$-adic Hodge theory - announcement
Integral $p$-adic Hodge theory - announcement
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积分 $p$-adic Hodge 理论 - 公告
DOI：
10.4310/mrl.2015.v22.n6.a3
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
P. Scholze
中科院分区：
文献类型：
--
作者：
B. Bhatt;M. Morrow;P. Scholze
给定$\mathbb C_p$的整数环上的一个适当的光滑（形式）概型，证明了如果其特殊纤维的晶上同调是无挠的，则其一般纤维的$p$-adic\'etale上同调也是无挠的.在这个公告中，我们勾勒的证明，这依赖于一个新的上同调理论之间的晶体和\'etale上同调插值的建设。进一步的细节和结果，包括比较同构，将在即将出版的完整文章中介绍。
Given a proper, smooth (formal) scheme over the ring of integers of $\mathbb C_p$, we prove that if the crystalline cohomology of its special fibre is torsion-free then the $p$-adic \'etale cohomology of its generic fibre is also torsion-free. In this announcement we sketch the proof, which relies on the construction of a new cohomology theory interpolating between crystalline and \'etale cohomology. Further details and results, including a comparison isomorphism, will be presented in the full forthcoming article.