DubTop Seminar: Toward chromatic Galois purity, II

Last time, I introduced Mathew's Galois theory of presentably symmetric monoidal stable \$\infty\$-categories, descendability, and chromatic Galois purity conjecture that the localization map \$L_nR\to L_1R\$ induces an equivalence on Galois groups for every \$\mathbb{E}_\infty\$-ring \$R\$. In this talk, I'll discuss how tools developed in the proof of the chromatic Nullstellensatz may be relevant to this conjecture. I'll talk about spectral Witt vectors and tilting, the construction of Lubin--Tate covers that detect nilpotence, and the circumstances in which these covers are descendable.