The E₂-term of the K(n)-local E_n-Adams spectral sequence

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• 作者：Tobias Barthel ; ^{tbarthel@mpim-bonn.mpg.de" class="auth_mail" title="E-mail the corresponding author} ; Drew Heard ; ^{drew.heard@mpim-bonn.mpg.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：K(n)K(n)-local homotopy theory ; Chromatic homotopy theory ; Morava E-theory ; Spectral sequence
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：15 June 2016
• 年：2016
• 卷：206
• 期：Complete
• 页码：190-214
• 全文大小：549 K

文摘

Let E=E_n$E=E_n$ be Morava E-theory of height n. In [8] Devinatz and Hopkins introduced the K(n)$K(n)$-local 54c0dfd317d8ea3dc05f079ca31" title="Click to view the MathML source">E_n$E_n$-Adams spectral sequence and showed that, under certain conditions, the E₂$E_2$-term of this spectral sequence can be identified with continuous group cohomology. We work with the category of L  -complete $E_{⁎}^{\vee }E$-comodules, and show that in a number of cases the E₂$E_2$-term of the above spectral sequence can be computed by a relative Ext group in this category. We give suitable conditions for when we can identify this Ext group with continuous group cohomology.