Differential fppf descent obstructions

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dc.contributor.advisorVoloch, José Felipe
dc.contributor.committeeMemberAllcock, Daniel
dc.contributor.committeeMemberCiperiani, Mirela
dc.contributor.committeeMemberKeel, Sean
dc.contributor.committeeMemberBuium, Alexandru
dc.creatorRezende De Macedo, Alessandro
dc.creator.orcid0000-0003-2009-9274
dc.date.accessioned2017-12-19T16:07:53Z
dc.date.available2017-12-19T16:07:53Z
dc.date.created2017-08
dc.date.issued2017-08-14
dc.date.submittedAugust 2017
dc.date.updated2017-12-19T16:07:54Z
dc.description.abstractIn this dissertation, we consider the category of schemes equipped with a derivation and investigate a differential analogue of the fppf site on a differential scheme. We interpret the obstruction to the existence of integral points in affine varieties given by certain differential equations introduced by Voloch as the descent obstruction associated with torsors under a certain sheaf for our differential fppf topology. We also consider a multiplicative analogue of those differential descent obstructions and show that it is the only obstruction to the existence of integral points in affine varieties over function fields. Finally, we describe the obstruction set in the case of smooth projective isotrivial curves of genus g > 1 over a function field, extending a result of Voloch.
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdf
dc.identifierdoi:10.15781/T2Z02ZR6V
dc.identifier.urihttp://hdl.handle.net/2152/63033
dc.language.isoen
dc.subjectAlgebraic geometry
dc.subjectFunction fields
dc.titleDifferential fppf descent obstructions
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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