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dc.contributor.advisorAberbach, Ianeng
dc.contributor.authorPolstra, Thomas Marioneng
dc.date.issued2017eng
dc.date.submitted2017 Springeng
dc.description.abstractThis dissertation establishes uniform bounds in characteristic p rings which are either F-finite or essentially of finite type over an excellent local ring. These uniform bounds are then used to show that the Hilbert-Kunz length functions and the normalized Frobenius splitting numbers defined on the spectrum of a ring converge uniformly to their limits, namely the Hilbert-Kunz multiplicity function and the Fsignature function. From this we establish that the F-signature function is lower semicontinuous. Lower semi-continuity of the F-signature of a pair is also established. We also give a new proof of the upper semi-continuity of Hilbert-Kunz multiplicity, a result originally proven by Ilya Smirnov.eng
dc.identifier.urihttps://hdl.handle.net/10355/61963
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.subject.FASTFPF ringseng
dc.titleUniform bounds in f-finite rings and their applicationseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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