3 papers
math.NT2025
On a non-abelian analogue of a conjecture of Michael Stoll
L. Alexander Betts
We formulate a non-abelian generalisation of a conjecture of Stoll, which conjecturally describes the structure of the loci cut out by Kim's method of non-abelian Chabauty. We prov…
math.NT2024
Local heights on hyperelliptic curves and quadratic Chabauty
L. Alexander Betts, Juanita Duque-Rosero, Sachi Hashimoto +1
Quadratic Chabauty is a -adic method for determining rational points on curves. Local heights are arithmetic invariants used in the quadratic Chabauty method. We present an algo…
math.NT2017
The motivic anabelian geometry of local heights on abelian varieties
L. Alexander Betts
We study the problem of describing local components of height functions on abelian varieties over characteristic local fields as functions on spaces of torsors under various re…