The homotopy fixed point spectra of profinite Galois extensions
The homotopy fixed point spectra of profinite Galois extensions
复制标题
有限伽罗瓦扩张的同伦不动点谱
DOI：
10.1090/s0002-9947-10-05154-8
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发表时间：
2008
影响因子：
1.3
通讯作者：
Daniel G. Davis
中科院分区：
文献类型：
--
作者：
M. Behrens;Daniel G. Davis
设E是一个E∞环谱a（在Rognes意义上）的k域无限g -伽罗瓦扩展。我们证明E可以看作是产生一个离散的g谱。同时，我们证明了如果E是满足一定附加条件的有利可图的k-局部定域扩展，则Rognes伽罗瓦对应的正向扩展到定域设置。我们表明,频谱函数F (E (hH) k, (E) k)相当于本地化同伦定点光谱((E | | G / H]])香港)k, k H和在哪里关闭子组G应用摩拉瓦河E-theory,包括显示Devinatz定义的同伦不动点和霍普金斯关闭子组定义的扩展摩拉瓦河稳定器集团同意那些对一个连续动作的不动点的派生函子。
Let E be a k-local profinite G-Galois extension of an E ∞ -ring spectrum A (in the sense of Rognes). We show that E may be regarded as producing a discrete G-spectrum. Also, we prove that if E is a profaithful k-local profinite extension which satisfies certain extra conditions, then the forward direction of Rognes's Galois correspondence extends to the profinite setting. We show that the function spectrum F A ((E hH ) k , (E hK ) k ) is equivalent to the localized homotopy fixed point spectrum ((E||G/H]]) hK ) k , where H and K are closed subgroups of G. Applications to Morava E-theory are given, including showing that the homotopy fixed points defined by Devinatz and Hopkins for closed subgroups of the extended Morava stabilizer group agree with those defined with respect to a continuous action in terms of the derived functor of fixed points.