Type
Text
Type
Dissertation
Advisor
Starr, Jason , Laza, Radu | Grushevsky, Samuel | de Jong, Johan.
Date
2012-05-01
Keywords
elementary obstructions, homogeneous spaces, rational curves, rationally simply connected, rational points | Mathematics
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71477
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
A basic question in arithmetic geometry is whether a variety defined over a non-closed field admits a rational point. When the base field is of geometric nature, i.e. | function fields of varieties, one hopes to solve the problem via purely algebraically geometric methods. In this thesis, we study the geometry of the moduli space of sections of a projective homogeneous space fibration over an algebraic curve. It leads to answers for the existence of rational points on projective homogeneous spaces defined either over a global function field or over a function field of a complex algebraic surface. | 88 pages
Recommended Citation
Zhu, Yi, "Homogeneous Fibrations over Curves" (2012). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 683.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/683