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UBC Theses and Dissertations
Distribution of integral points on varieties Coccia, Simone
Abstract
One of the guiding principles in Diophantine geometry is that, if an algebraic variety contains "many" integral points, then there is a geometric reason explaining their abundance. In this thesis we will focus on two geometric notions of abundance for integral points, namely Zariski density and the Hilbert Property, the latter being a generalization of Hilbert's irreducibility theorem to arbitrary algebraic varieties. We will focus on the case of complements of anticanonical divisors in smooth del Pezzo surfaces, proving that the integral points are always potentially dense and that the Hilbert Property holds, potentially, when such a complement is simply connected. We will also discuss joint work of Dragos Ghioca and the author that led to the proof of the Drinfeld modules analogue of Siegel's theorem on the finiteness of integral points.
Item Metadata
Title |
Distribution of integral points on varieties
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Creator | |
Supervisor | |
Publisher |
University of British Columbia
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Date Issued |
2024
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Description |
One of the guiding principles in Diophantine geometry is that, if an algebraic variety contains "many" integral points, then there is a geometric reason explaining their abundance. In this thesis we will focus on two geometric notions of abundance for integral points, namely Zariski density and the Hilbert Property, the latter being a generalization of Hilbert's irreducibility theorem to arbitrary algebraic varieties. We will focus on the case of complements of anticanonical divisors in smooth del Pezzo surfaces, proving that the integral points are always potentially dense and that the Hilbert Property holds, potentially, when such a complement is simply connected. We will also discuss joint work of Dragos Ghioca and the author that led to the proof of the Drinfeld modules analogue of Siegel's theorem on the finiteness of integral points.
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Genre | |
Type | |
Language |
eng
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Date Available |
2024-04-12
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0441329
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2024-05
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International