阿贝尔紧李群的等变Landweber正合函子定理
An Equivariant Landweber Exact Functor Theorem for Abelian Compact Lie Groups
- Nankai University（南开大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文为阿贝尔紧李群证明了等变Landweber正合函子定理，给出分次模成为同调理论的充要条件，并应用证明Wisdom猜想。
AI中文摘要：
我们证明了阿贝尔紧李群$G$的等变Landweber正合函子定理。对于$G$-等变Lazard环$L_G$上的分次模$N$，我们给出了$N$上使得函子\\[ X\longmapsto (MU_G)_*(X)\otimes_{L_G} N \\] 在真$G$-谱范畴$\mathrm{Sp}^G$上定义同调理论的必要且充分的代数条件。我们的判据是通过在由$G$的闭子群索引的每个分层上验证Landweber正合性，然后通过Euler类粘合局部平坦性数据而获得的。作为应用，我们证明对于任何非等变Landweber正合环谱$E$，$MU_G\wedge_{MU} E$是等变Landweber正合的，从而证明了Wisdom的一个猜想。
英文摘要：
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 \[ X\longmapsto (MU_G)_*(X)\otimes_{L_G} N \] to define a homology theory on the category $\mathrm{Sp}^G$ 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 $E$, $MU_G\wedge_{MU} E$ is equivariantly Landweber exact, thereby proving a conjecture of Wisdom.
