Persistent Link:
http://hdl.handle.net/10150/238653
Title:
Nonexistence of Rational Points on Certain Varieties
Author:
Nguyen, Dong Quan Ngoc
Issue Date:
2012
Publisher:
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:
text; Electronic Dissertation
Keywords:
del Pezzo surfaces; Hasse principle; hyperelliptic curves; K3 surfaces; Mathematics; Azumaya algebras; Brauer-Manin obstruction
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Sharifi, Romyar T.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleNonexistence of Rational Points on Certain Varietiesen_US
dc.creatorNguyen, Dong Quan Ngocen_US
dc.contributor.authorNguyen, Dong Quan Ngocen_US
dc.date.issued2012-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © 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.en_US
dc.description.abstractIn 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.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectdel Pezzo surfacesen_US
dc.subjectHasse principleen_US
dc.subjecthyperelliptic curvesen_US
dc.subjectK3 surfacesen_US
dc.subjectMathematicsen_US
dc.subjectAzumaya algebrasen_US
dc.subjectBrauer-Manin obstructionen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorSharifi, Romyar T.en_US
dc.contributor.committeememberSharifi, Romyar T.en_US
dc.contributor.committeememberCais, Bryden R.en_US
dc.contributor.committeememberMadden, Danielen_US
dc.contributor.committeememberMcCallum, William G.en_US
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