- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Points of small height on affine varieties defined...
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
Points of small height on affine varieties defined over function fields of finite transcendence degree Nguyen, Dac Nhan Tam
Abstract
The problem of this thesis concerns points of small height on affine varieties defined over arbitrary function fields, and is based on published work with Prof. Dragos Ghioca (see [GN20]). The main result is as follows: the points lying outside the largest subvariety defined over the constant field cannot have arbitrarily small height. Prior results of this type include [Ghi09], [Ghi14]. In particular, [Ghi14] answers this question for function fields of transcendence degree 1. It also captures the history of the subject and features an argument that was initially used by the author of this thesis to extend [Ghi14] to varieties defined over function fields of arbitrary (finite) transcendence degree. The content of this thesis and the associated published paper not only extends [Ghi14] to arbitrary transcendence degree, but also provides a sharp lower bound for points which are not contained in the largest subvariety defined over the constant field. The argument here works directly with the defining polynomials of the variety (compare with [Ghi14]), and the lower bound only depends on their degrees.
Item Metadata
Title |
Points of small height on affine varieties defined over function fields of finite transcendence degree
|
Creator | |
Supervisor | |
Publisher |
University of British Columbia
|
Date Issued |
2022
|
Description |
The problem of this thesis concerns points of small height on affine varieties defined over arbitrary function fields, and is based on published work with Prof. Dragos Ghioca (see [GN20]). The main result is as follows: the points lying outside the largest subvariety defined over the constant field cannot have arbitrarily small height.
Prior results of this type include [Ghi09], [Ghi14]. In particular, [Ghi14] answers this question for function fields of transcendence degree 1. It also captures the history of the subject and features an argument that was initially used by the author of this thesis to extend [Ghi14] to varieties defined over function fields of arbitrary (finite) transcendence degree. The content of this thesis and the associated published paper not only extends [Ghi14] to arbitrary transcendence degree, but also provides a sharp lower bound for points which are not contained in the largest subvariety
defined over the constant field. The argument here works directly with the defining polynomials of the variety (compare with [Ghi14]), and the lower bound only depends on their degrees.
|
Genre | |
Type | |
Language |
eng
|
Date Available |
2022-04-13
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0412780
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Graduation Date |
2022-05
|
Campus | |
Scholarly Level |
Graduate
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International