{"id":{"repo_id":"missouri","oai_identifier":"oai:mospace.umsystem.edu:10355/61963"},"canonical_url":"https://search.dev.ndltd.org/etd/missouri/oai:mospace.umsystem.edu:10355/61963","repository":{"repo_id":"missouri","name":"University of Missouri","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Uniform bounds in F-finite rings and their applications /","abstract":"This 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.","abstract_html":"This 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.","abstract_has_math":false,"creators":["Polstra, Thomas Marion"],"institution":"University of Missouri--Columbia","degree_name":"Ph. 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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."]},{"key":"dc:title","label":"Title","values":["Uniform bounds in F-finite rings and their applications /"]}]}],"canonical_facts":{"dc:contributor.advisor":["Aberbach, Ian M."],"dc:creator":["Polstra, Thomas Marion"],"dc:date.accessioned":["2017-11-02T14:54:58Z"],"dc:date.available":["2017-11-02T14:54:58Z"],"dc:date.issued":["2017"],"dc:description.abstract":["This 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."],"dc:identifier.doi":["https://doi.org/10.32469/10355/61963"],"dc:identifier.uri":["https://hdl.handle.net/10355/61963"],"dc:language":["English"],"dc:language.iso":["eng"],"dc:publisher":["University of Missouri--Columbia"],"dc:rights":["OpenAccess."],"dc:title":["Uniform bounds in F-finite rings and their applications /"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics (MU)"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["University of Missouri--Columbia"]},"updated_at":"2026-07-24T03:07:13Z"}