Derived completion for comodules
Derived completion for comodules
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DOI：
10.1007/s00229-018-1094-0
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发表时间：
2018-08
影响因子：
0.6
通讯作者：
T. Barthel;Drew Heard;Gabriel Valenzuela
中科院分区：
文献类型：
--
作者：
T. Barthel;Drew Heard;Gabriel Valenzuela
本文的目的是引入和研究Hopf代数体上余模的完备性和局部同调，推广了Greenlees和May在离散情形下的工作。特别地，我们将模论与余模理论完备化联系起来，构造了各种局部同调谱序列，并给出了模的局部对偶的倾斜理论解释。我们的结果转化为全局商栈上的准相干层，并提供了一种新的方法来解色分裂猜想。
The objective of this paper is to introduce and study completions and local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete case. In particular, we relate module-theoretic to comodule-theoretic completion, construct various local homology spectral sequences, and derive a tilting-theoretic interpretation of local duality for modules. Our results translate to quasi-coherent sheaves over global quotient stacks and feed into a novel approach to the chromatic splitting conjecture.