论文标题
派生的变形理论
Operads in Derived Deformation Theory
论文作者
论文摘要
Pridham和Lurie的定理提供了形式模量问题与特征零的代数之间的等效性。在他的作品中，卢里（Lurie）在正式模量问题中出现的代数出现的公理需要使$ \ mathbb {e} _ \ infty $ -algebras使用Koszul duality的化合物，并在$ \ iffty $ -operads的情况下使用。 Calaque-campos-nuiten的最新工作扩展了Lurie的工作，以获得由彩色的Operad参数参数的正式模量问题与Koszul Dual Dual Operad上的代数。这个手稿既是教学的说明，又是对他们的作品的质疑，并具有谦虚但原始的支持引理。
A theorem by Pridham and Lurie provides an equivalence between formal moduli problems and Lie algebras in characteristic zero. In his work, Lurie has distilled the axioms that the algebras appearing in the formal moduli problem need to satisfy, and worked out the case of $\mathbb{E}_\infty$-algebras using an incarnation of the Koszul duality, in the setting of $\infty$-operads. The more recent work of Calaque-Campos-Nuiten extends Lurie's work to obtain an equivalence between formal moduli problem parameterized by a colored operad, and algebras over its Koszul dual operad. This manuscript is both, a pedagogical exposition, and a questioning of their work, with modest, but original, supporting lemmas.
