论Lurie定理及其应用
On Lurie's theorem and applications
AI总结：
本文整合Lurie近期工作中的相关要素，证明了作为经典Landweber正合函子定理全局高阶范畴改进的Lurie定理，并讨论了其在Lubin--Tate理论等领域的应用。
摘要：
Lurie定理指出，在高度为$n$的$p$-可除群的模叠上的形式平展Deligne--Mumford叠的site上，存在一个环谱层，它在仿射概形上与经典的Landweber正合函子定理（LEFT，Landweber exact functor theorem）一致。换言之，该定理是LEFT的一种全局的、高阶范畴化的改进。在近期工作中，Lurie引入了证明该定理所需的诸多要素，本文将这些要素整合起来，证明了Lurie定理。文中还讨论了该定理在Lubin--Tate理论、拓扑模形式与自守形式以及Adams运算中的应用。
英文摘要：
Lurie's theorem states that there exists a sheaf of ring spectra on the site of formally étale Deligne--Mumford stacks over the moduli stack of $p$-divisible groups of height $n$, which agrees with the classical Landweber exact functor theorem (LEFT) on affines. In other words, this theorem is a global, higher categorical refinement of the LEFT. In recent work, Lurie has introduced many of the ingredients one needs to prove this theorem, and in this article, we gather these ingredients together and prove Lurie's theorem. Applications of this theorem to Lubin--Tate theories, topological modular and automorphism forms, and Adams operations are also discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
