Points on Curves with Small Galois Group (POSTPONED)

James Rawson (University of Warwick/Glasgow)

Wednesday 8th October 16:00-17:00
Maths 311B

Abstract

Faltings' Theorem says that a curve of genus 2 has only finitely many points defined over a fixed number field. One generalisation of this statement is to allow the number field to vary over all number fields of fixed degree, and ask if there are still finitely many points or not. Work of Abramovich—Harris and Kadets—Vogt show that the answer to this question is again controlled by the geometry of the curve. In this talk we will consider a refinement of this question - instead of varying the number field over all number fields of fixed degree, we instead vary only over those with fixed degree and Galois group. I will explore the case of cubic fields with Galois group Z/3Z, as well as what can be expected for the Galois groups arising for degree 4 fields. 

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