Smith, Marshall2024-03-292024-03-292024-02https://hdl.handle.net/11299/261996University of Minnesota Ph.D. dissertation. February 2024. Major: Mathematics. Advisor: Craig Westerland. 1 computer file (PDF); iii, 126 pages.Using a form of Galois descent, we construct a family of spectral sequences computingthe homotopy groups of the Picard space Picn whose 0th homotopy group is the Picard group of the K(n)-local category. For all primes p and heights n, we compute the rank of π∗Picn ⊗Zp Qp to be zero for ∗ ≥ 2 and 1 for ∗ = 1. Finally, using these methods, we describe the rank of π0Pic ⊗Zp Qp in terms of a limit of module categories and discuss implications involving the algebraic Picard group.enThesis or Dissertation