Nonexistence of Rational Points on Certain Varieties
Issue Date
2012Keywords
del Pezzo surfacesHasse principle
hyperelliptic curves
K3 surfaces
Mathematics
Azumaya algebras
Brauer-Manin obstruction
Advisor
Sharifi, Romyar T.Metadata
Show full item recordPublisher
The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Abstract
In this thesis, we study the Hasse principle for curves and K3 surfaces. We give several sufficient conditions under which the Brauer-Manin obstruction is the only obstruction to the Hasse principle for curves and K3 surfaces. Using these sufficient conditions, we construct several infinite families of curves and K3 surfaces such that these families are counterexamples to the Hasse principle that are explained by the Brauer-Manin obstruction.Type
textElectronic Dissertation
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Graduate CollegeMathematics