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2020 An unstable change of rings for Morava $E$–theory
Robert Thompson
Algebr. Geom. Topol. 20(5): 2145-2176 (2020). DOI: 10.2140/agt.2020.20.2145

Abstract

The Bousfield–Kan (or unstable Adams) spectral sequence can be constructed for various homology theories, such as Brown–Peterson homology theory BP , Johnson–Wilson theory E ( n ) or Morava E –theory E n . For nice spaces the E 2 –term is given by Ext in a category of unstable comodules. We establish an unstable Morava change of rings isomorphism between Ext 𝒰 Γ B ( B , M ) and Ext 𝒰 E n E n I n ( E n I n , E n BP M ) , where ( B , Γ B ) denotes the Hopf algebroid ( v n 1 BP I n , v n 1 BP BP I n ) . We show that the latter groups can be interpreted as Ext in the category of continuous modules over the profinite monoid of endomorphisms of the Honda formal group law. By comparing this with the cohomology of the Morava stabilizer group we obtain an unstable Morava vanishing theorem when p 1 n

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Robert Thompson. "An unstable change of rings for Morava $E$–theory." Algebr. Geom. Topol. 20 (5) 2145 - 2176, 2020. https://doi.org/10.2140/agt.2020.20.2145

Information

Received: 20 September 2014; Revised: 24 August 2019; Accepted: 8 September 2019; Published: 2020
First available in Project Euclid: 10 November 2020

MathSciNet: MR4171565
Digital Object Identifier: 10.2140/agt.2020.20.2145

Subjects:
Primary: 55N20, 55Q51, 55T15

Rights: Copyright © 2020 Mathematical Sciences Publishers

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