Uniform bounds in F-finite rings and their applications /

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics (MU)

Grantor dc:publisher

University of Missouri--Columbia

Year dc:date.issued

2017

Author dc:creator

• Polstra, Thomas Marion

Advisor dc:contributor.advisor

• Aberbach, Ian M.

Statement dc:rights

• OpenAccess.

Language dc:language.iso

eng, English

DOI

https://doi.org/10.32469/10355/61963

OAI identifier oai:identifier

oai:mospace.umsystem.edu:10355/61963