Online Archive of University of Virginia Scholarship
Uniform Convergence Methods in Hilbert-Kunz Theory1308 views
Author
Smirnov, Ilya, Mathematics - Graduate School of Arts and Sciences, University of Virginia
Advisors
Huneke, Craig, Department of Mathematics, University of Virginia
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.
Smirnov, Ilya. Uniform Convergence Methods in Hilbert-Kunz Theory. University of Virginia, Mathematics - Graduate School of Arts and Sciences, PHD (Doctor of Philosophy), 2015-04-16, https://doi.org/10.18130/V31G1T.
