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PreprintCC BY 4.0arXiv

An Equivariant Landweber Exact Functor Theorem for Abelian Compact Lie Groups

  • Yingxin Li
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Abstract

We prove an equivariant Landweber exact functor theorem for abelian compact Lie groups G. For a graded module N over the G-equivariant Lazard ring LG, we give necessary and sufficient algebraic conditions on N for the functor Xlongmapsto (MUG)*(X)⊗LG N to define a homology theory on the category SpG of genuine G-spectra. Our criterion is obtained by varifying the Landweber exactness on each stratum indexed by a closed subgroup of G and then gluing the local flatness data via Euler classes. As an application, we show that for any non-equivariant Landweber exact ring spectrum E, MUG∧MU E is equivariantly Landweber exact, thereby proving a conjecture of Wisdom.

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Cite

BibTeXRIS
BibTeX
@misc{li2026equivariant,
  title = {{An Equivariant Landweber Exact Functor Theorem for Abelian Compact Lie Groups}},
  author = {Yingxin Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17519},
  eprint = {2609.17519},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17519},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An Equivariant Landweber Exact Functor Theorem for Abelian Compact Lie Groups
AU  - Yingxin Li
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17519
UR  - https://arxiv.org/abs/2609.17519
AB  - We prove an equivariant Landweber exact functor theorem for abelian compact Lie groups G. For a graded module N over the G-equivariant Lazard ring L_G, we give necessary and sufficient algebraic conditions on N for the functor Xlongmapsto (MU_G)_*(X)⊗_L_G N to define a homology theory on the category Sp^G of genuine G-spectra. Our criterion is obtained by varifying the Landweber exactness on each stratum indexed by a closed subgroup of G and then gluing the local flatness data via Euler classes. As an application, we show that for any non-equivariant Landweber exact ring spectrum E, MU_G∧_MU E is equivariantly Landweber exact, thereby proving a conjecture of Wisdom.
ER  -