标题： 拓扑模形式的下降谱序列 显示英文标题

标题： The descent spectral sequence for topological modular forms

摘要： 我们证明了拓扑模形式谱的间隙定理$\mathrm{Tmf}$。这消除了文献中长期存在的循环性，从而确认了霍普金斯和马豪尔二十多年前对$\pi_\ast \mathrm{tmf}$的计算。我们的方法至关重要的是现代的方法，发展并改进了许多合成谱中的技术。 显示英文摘要

摘要： We prove the Gap Theorem for the spectrum of topological modular forms $\mathrm{Tmf}$. This removes a longstanding circularity in the literature, thereby confirming the computation of $\pi_\ast \mathrm{tmf}$ from over two decades ago by Hopkins and Mahowald. Our approach is crucially a modern one, developing and refining many techniques in synthetic spectra.