Galois descent and the rational homotopy of the K(n)-local Picard space
2024-02
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Galois descent and the rational homotopy of the K(n)-local Picard space
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2024-02
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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.
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University of Minnesota Ph.D. dissertation. February 2024. Major: Mathematics. Advisor: Craig Westerland. 1 computer file (PDF); iii, 126 pages.
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Smith, Marshall. (2024). Galois descent and the rational homotopy of the K(n)-local Picard space. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/261996.
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