Counting rational points on genus one curves
Licentiatavhandling, 2017

This thesis contains two papers dealing with counting problems for curves of genus one. We obtain uniform upper bounds for the number of rational points of bounded height on such curves. The main tools to study these problems are descent and various refined versions of Heath-Brown’s p-adic determinant method. In the first paper, we count rational points on smooth plane cubic curves. In the second paper, we count rational points on non-singular complete intersections of two quadrics. The methods are different for curves of small height and large height and descent is only used for curves of small height.

genus

rational points

Diophantine equations

determinant method

descent

cubic and quartic curves

Elliptic curves

Pascal, Matematiska vetenskaper, Chalmers tvärgata 3
Opponent: Dr Oscar Marmon, University of Copenhagen, Denmark

Författare

Manh Hung Tran

Chalmers, Matematiska vetenskaper, Algebra och geometri

Manh Hung Tran, Counting rational points on smooth cubic curves

Manh Hung Tran, Uniform bounds for rational points on complete intersections of two quadric surfaces

Ämneskategorier

Geometri

Utgivare

Chalmers tekniska högskola

Pascal, Matematiska vetenskaper, Chalmers tvärgata 3

Opponent: Dr Oscar Marmon, University of Copenhagen, Denmark