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Title: Rational points in function fields
Author: Manzateanu, Adelina
ISNI:       0000 0004 8500 0201
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2019
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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.
Supervisor: Booker, Andrew ; Browning, Tim Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: number theory ; function fields ; rational points ; rational curves ; Manin's conjecture ; Peyre's constant ; 0-cycles