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Kovács, Sándor Godfrey, Charles W 2021-08-26T18:13:03Z 2021-08-26T18:13:03Z 2021-08-26 2021 Godfrey_washington_0250E_22750.pdf http://hdl.handle.net/1773/47629 Thesis (Ph.D.)--University of Washington, 2021 This document consists of three mathematically independent and more or less thematically independent parts. Chapter 1 concerns invariance of the cohomology groups of divisorial ideal sheaves under (a restricted class of) birational morphisms of pairs in arbitrary characteristic, and as an application extends some foundational results in the theory of rational pairs that were previously known only in characteristic 0. Chapter 2 discusses correspondences in logarithmic Hodge theory related to an as-of-yet-unsuccessful alternative strategy for proving the main theorems of Chapter 1. Chapter 3 introduces and studies a condition on a proper scheme over a field of positive characteristic defined in terms of the Frobenius action, which we call globally F-full. application/pdf en_US CC BY-SA birational geometry F-singularities Frobenius techniques Grothendieck duality Hodge theory simplicial methods Mathematics Mathematics Higher direct images of ideal sheaves, correspondences in log Hodge cohomology and globally F-full varieties Thesis Open Access open.access