A note on Sen's theory in the imperfect residue field case
A note on Sen's theory in the imperfect residue field case
复制标题
对森理论在不完美残渣场情况下的注记
DOI：
10.1007/s00209-010-0726-1
复制
发表时间：
2011
影响因子：
0.8
通讯作者：
Shun
中科院分区：
文献类型：
--
作者：
OHKUBO;Shun
在Sen的理论中，在不完美剩余域的情况下，Brinon定义了一个函子，从-表示范畴到某个李代数的线性表示范畴。给出了-表示的连续伽罗瓦上同调与相应表示的李代数上同调的一个比较定理。证明的关键成分是Hyodo的伽罗瓦上同调的计算和可解李代数的李代数上同调的可擦性。
In Sen’s theory in the imperfect residue field case, Brinon defined a functor from the category of-representations to the category of linear representations of a certain Lie algebra. We give a comparison theorem between the continuous Galois cohomology of-representations and the Lie algebra cohomology of the associated representations. The key ingredients of the proof are Hyodo’s calculation of Galois cohomology and the effaceability of Lie algebra cohomology for solvable Lie algebras.