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Uniform Convergence Methods in Hilbert-Kunz Theory

Smirnov, Ilya
Format
Thesis/Dissertation; Online
Author
Smirnov, Ilya
Advisor
Huneke, Craig
Abstract
Hilbert-Kunz multiplicity is an invariant of a local ring containing a field of positive characteristic. In this work, we study its continuity properties as a function on a variety. First, we develop a theory of equimultiplicity for Hilbert-Kunz multiplicity. Remarkably, it is quite similar to the classical equimultiplicity. The theory is then applied to show that a stronger form of upper semi-continuity does not hold. Later, using uniform convergence ideas we prove that a weaker form of upper semi-continuity holds. As an application, we obtain that the maximum value locus of Hilbert-Kunz multiplicity is closed.
Language
English
Published
University of Virginia, Department of Mathematics, PHD, 2015
Published Date
2015-04-16
Degree
PHD
Collection
Libra ETD Repository
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