Rational points in function fields

  • Adelina Manzateanu

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)

Abstract

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 Award1 Oct 2019
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorAndrew R Booker (Supervisor) & Tim Browning (Supervisor)

Keywords

  • number theory
  • function fields
  • rational points
  • rational curves
  • Manin's conjecture
  • Peyre's constant
  • 0-cycles

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