A function field version of the circle method is applied to a cubic hypersurface X defined over a finite field Fq. Using the correspondence between Fq-rational curves and Fq(t)-points, we deduce the dimension and irreducibility of the moduli space of rational curves on X passing through two fixed points. Furthermore, we study Manin’s conjecture over function fields and obtain an example where the conjecture holds after removing a thin set of points. This leads to an application which can be seen as the prime number theorem for 0-cycles on P2.
| Date of Award | 1 Oct 2019 |
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| Original language | English |
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| Awarding Institution | |
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| Supervisor | Andrew R Booker (Supervisor) & Tim Browning (Supervisor) |
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- number theory
- function fields
- rational points
- rational curves
- Manin's conjecture
- Peyre's constant
- 0-cycles
Rational points in function fields
Manzateanu, A. (Author). 1 Oct 2019
Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)