Studying points on varieties via varying families

  • 25 October 2023
  • 1500-1600
  • Sch 1.05

Alex Torzewski (KCL)

We show how Lawrence-Venkatesh's method for studying points on a variety X can be applied to curves in families. In the process, we also outline the original method. The idea is that if there exists a family over X which varies "a lot", then this strongly constrains the existence of points. This is an example of how topology influences arithmetic, in this case via differential equations! 


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