导出代数几何中的Tannakian重构
Tannakian reconstruction in derived algebraic geometry
AI总结：
该研究在以动画环谱为基本对象的导出代数几何中，用Nuiten–Toën的$\u0398$-范畴替代对称幺半$\u221e$-范畴，证明了Lurie及Bhatt–Halpern-Leistner的Tannakian重构定理的类似结论，刻画了动画环的严格交换结构。
AI中文摘要：
我们在导出代数几何中证明了Lurie以及Bhatt--Halpern-Leistner的Tannakian重构定理的类似结论，该领域的基本几何对象是动画环的谱，而非$\u2112_\u221e$-环。在此设定下，对称幺半$\u221e$-范畴被替换为Nuiten--Toën的$\u0398$-范畴。后者是对称幺半$\u221e$-范畴的增强，可捕捉动画环上的严格交换结构。
英文摘要：
We prove analogues of Tannakian reconstruction theorems of Lurie and Bhatt--Halpern-Leistner in \emph{derived} algebraic geometry, where the basic geometric objects are spectra of animated rings rather than $\mathbb{E}_\infty$-rings. In this setting, symmetric monoidal $\infty$-categories are replaced by the $Θ$-categories of Nuiten--Toën. These are enhancements of symmetric monoidal $\infty$-categories which capture the strict commutativity structure on animated rings.
