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arXiv · 2401.12227

Properties and Examples of $A$-Landweber Exact Spectra

Noah Wisdom
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Abstract

It is classically known that Landweber exact homology theories (complex oriented theories which are completely determined by complex cobordism) admit no nontrivial phantom maps. Herein we propose a definition of $A$-Landweber exact spectra, for $A$ a compact abelian Lie group, and show that an analogous result on phantom maps holds. Also, we show that a conjecture of May on $KU_G$ is false. We do not prove an equivariant Landweber exact functor theorem, and therefore our result on phantom maps only applies to $MU_A$, $KU_A$, their $p$-localizations, and $BP_A$, which are shown to be $A$-Landweber exact by ad-hoc methods.

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Noah Wisdom. 2024-01-12. Properties and Examples of $A$-Landweber Exact Spectra. https://arxiv.org/abs/2401.12227

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