Brian Lawrence

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math.NT2025

The Shafarevich conjecture for hypersurfaces in abelian varieties

Brian Lawrence, Will Sawin

Faltings proved that there are finitely many abelian varieties of genus $g$ over a number field $K$ , with good reduction outside a finite set of primes $S$ . Fixing one of these abe…

math.NT2024

Conditional algorithmic Mordell

Levent AlpÃ¶ge, Brian Lawrence

We specify a Turing machine $T_{Mordell}$ with the following properties. 1. On input $(K, C / K)$ , with $K / Q$ a number field and $C / K$ a smooth projective hyperbolic c…