Wisdom’s conjecture on equivariant Landweber exactness
For every abelian compact Lie group and every non-equivariantly Landweber exact ring spectrum , the genuine -equivariant ring spectrum is equivariantly Landweber exact; equivalently, the associated functor defines a homology theory on genuine -spectra, where is the -module associated to .
References
Primary source
Additional references
- An Equivariant Landweber Exact Functor Theorem for Abelian Compact Lie Groups — arXiv — Yingxin Li
Progress summary
A September 2026 preprint claims to settle the conjecture, but the result has not yet been independently checked.
Wisdom’s conjecture asks whether every non-equivariantly Landweber exact spectrum makes equivariantly Landweber exact for an abelian compact Lie group . Noah Wisdom formulated this general statement in 2024 but explicitly did not prove an equivariant Landweber exact functor theorem.
Known results
- Wisdom, 2024: proved equivariant Landweber exactness for several specific spectra, including , , and , by separate methods.
- Wisdom, 2024: established the conjecture for , but left the general case open.
September 2026 claimed solution
A September 2026 preprint by Yingxin Li claims necessary and sufficient algebraic conditions for equivariant Landweber exactness and claims, in particular, that is equivariantly Landweber exact for every non-equivariantly Landweber exact . This would settle Wisdom’s conjecture for abelian compact Lie groups, but the claim is supported only by an unrefereed preprint.
Current status (as of September 2026): A preprint claims the conjecture is proved for abelian compact Lie groups, while the claim remains unverified.
Solutions 0
No solutions have been posted yet.