ON MU-HOMOLOGY OF CONNECTIVE MODELS OF HIGHER REAL K-THEORIES

Christian Carrick; Michael A. Hill

doi:10.1090/bproc/265

ON MU-HOMOLOGY OF CONNECTIVE MODELS OF HIGHER REAL K-THEORIES

Christian Carrick
, Michael A. Hill

University of Minnesota

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We use the slice filtration to study the MU-homology of the fixed points of connective models of Lubin-Tate theory studied by Hill, Hopkins, and Ravenel and Beaudry, Hill, Shi, and Zeng. We show that, unlike their periodic counterparts EO_nthe MU homology of BP^((G))〈m〉^Gusually fails to be even and torsion free. This can only happen when the height n = m|G|/2 is less than 3, and in the edge case n = 2, we show that this holds for tmf0(3) but not for tmf0(5), and we give a complete computation of the MU*MU-comodule algebra MU*tmf0(3).

Original language	English
Pages (from-to)	172-186
Number of pages	15
Journal	Proceedings of the American Mathematical Society, Series B
Volume	12
Issue number	1
DOIs	https://doi.org/10.1090/bproc/265
Publication status	Published - 10 Jul 2025

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ON MU-HOMOLOGY OF CONNECTIVE MODELS OF HIGHER REAL K-THEORIESFinal published version, 267 KBLicence: CC BY

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abstract = "We use the slice filtration to study the MU-homology of the fixed points of connective models of Lubin-Tate theory studied by Hill, Hopkins, and Ravenel and Beaudry, Hill, Shi, and Zeng. We show that, unlike their periodic counterparts EOnthe MU homology of BP((G))〈m〉Gusually fails to be even and torsion free. This can only happen when the height n = m|G|/2 is less than 3, and in the edge case n = 2, we show that this holds for tmf0(3) but not for tmf0(5), and we give a complete computation of the MU*MU-comodule algebra MU*tmf0(3).",

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ON MU-HOMOLOGY OF CONNECTIVE MODELS OF HIGHER REAL K-THEORIES

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