Crystalline cohomology of algebraic stacks and Hyodo-Kato cohomology
Crystalline cohomology of algebraic stacks and Hyodo-Kato cohomology
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代数栈的晶体上同调和 Hyodo-Kato 上同调
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发表时间：
2018
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通讯作者：
Martin Olsson
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文献类型：
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作者：
Martin Olsson
本文利用堆栈理论技术研究了p进域上适当光滑格式的de Rham上同调晶体结构及其在p进Hodge理论中的应用。他发展了代数堆的晶体上同调和de Rham- witt配合的一般理论，并将其应用于de Rham上同调的（[phi]， N， G）-结构的构造和研究。使用堆栈理论的观点而不是对数几何，他发展了证明cst猜想所需的成分，使用Fontaine， Messing, Hyodo， Kato和Tsuji的方法，除了p进消失循环的关键计算。他还将单算子的构造推广到具有比半稳定更一般约简类型的方案上，并证明了伽罗瓦对上同调作用的驯服性的新结果。
In this text the author uses stack-theoretic techniques to study the crystalline structure on the de Rham cohomology of a proper smooth scheme over a p-adic field and applications to p-adic Hodge theory. He develops a general theory of crystalline cohomology and de Rham-Witt complexes for algebraic stacks and applies it to the construction and study of the ([phi], N, G)-structure on de Rham cohomology. Using the stack-theoretic point of view instead of log geometry, he develops the ingredients needed to prove the Cst-conjecture using the method of Fontaine, Messing, Hyodo, Kato, and Tsuji, except for the key computation of p-adic vanishing cycles. He also generalizes the construction of the monodromy operator to schemes with more general types of reduction than semistable and proves new results about tameness of the action of Galois on cohomology.