Translator Disclaimer
2020 Invertible $K(2)$–local $E$–modules in $C_4$–spectra
Agnès Beaudry, Irina Bobkova, Michael Hill, Vesna Stojanoska
Algebr. Geom. Topol. 20(7): 3423-3503 (2020). DOI: 10.2140/agt.2020.20.3423

Abstract

We compute the Picard group of the category of K(2)–local module spectra over the ring spectrum EhC4, where E is a height 2 Morava E–theory and C4 is a subgroup of the associated Morava stabilizer group. This group can be identified with the Picard group of K(2)–local E–modules in genuine C4–spectra. We show that in addition to a cyclic subgroup of order 32 generated by ES1, the Picard group contains a subgroup of order 2 generated by ES7+σ, where σ is the sign representation of the group C4. In the process, we completely compute the RO(C4)–graded Mackey functor homotopy fixed point spectral sequence for the C4–spectrum E.

Citation

Download Citation

Agnès Beaudry. Irina Bobkova. Michael Hill. Vesna Stojanoska. "Invertible $K(2)$–local $E$–modules in $C_4$–spectra." Algebr. Geom. Topol. 20 (7) 3423 - 3503, 2020. https://doi.org/10.2140/agt.2020.20.3423

Information

Received: 14 January 2019; Revised: 16 September 2019; Accepted: 22 October 2019; Published: 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194286
Digital Object Identifier: 10.2140/agt.2020.20.3423

Subjects:
Primary: 55P42, 55Q91
Secondary: 20J06, 55M05, 55P60, 55Q51

Rights: Copyright © 2020 Mathematical Sciences Publishers

JOURNAL ARTICLE
81 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.20 • No. 7 • 2020
MSP
Back to Top