Geometry and Topology Seminar ——The inverse limit topology and profinite descent on $K(n)$-local Picard groups
报告人：张凝川 (Indiana Universty Bloomington)
时间：2023-12-27 15:10-17:00
地点：智华楼四元厅（224, 225）
Abstract: In this talk, we give an $\infty$-categorical explanation of the inverse limit topology on Picard groups of $K(n)$-local ring spectra. Building upon Burklund's result on the multiplicative structures of generalized Moore spectra, we prove that the module category over a $K(n)$-local commutative ring spectrum is equivalent to the limit of its base changes by a tower of generalized Moore spectra of type $n$. As a result, $K(n)$-local Picard groups are endowed with a natural inverse limit topology. This topology allows us to identify the entire $E_1$ and $E_2$-pages of a descent spectral sequence for Picard spaces of $K(n)$-local profinite Galois extensions. This is joint work with Guchuan Li.
