论文标题
关于Lurie的定理和应用程序
On Lurie's theorem and applications
论文作者
论文摘要
Lurie的定理指出，在正式的典型Deligne-Mumford堆叠的地点上存在着一条环形光谱 - $ p $ $ n $的Moduli堆栈中，高度$ n $的群，与经典的Landweber Landweber Exact functor Theorem（左）一致。换句话说，该定理是对左派的全球性，更高的分类完善。在最近的工作中，Lurie介绍了证明该定理所需的许多成分，在本文中，我们将这些成分聚集在一起并证明了Lurie的定理。还讨论了该定理在润滑理论，拓扑模块化和自动形态形式以及Adams操作中的应用。
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.
