15 citations · 16 across the 8 of their papers we have counts for
10 papers
Conditional algorithmic Mordell
Levent Alpöge, Brian Lawrence
We specify a Turing machine with the following properties. 1. On input , with a number field and a smooth projective hyperbolic c…
Sparsity of Integral Points on Moduli Spaces of Varieties
Jordan S. Ellenberg, Brian Lawrence, Akshay Venkatesh
Let be a quasi-projective variety over a number field, admitting (after passage to ) a geometric variation of Hodge structure whose period mapping has zero-dimensio…
Nonvanishing of Central Derivatives of Modular -series in Level
Brian Lawrence
A quadratic twist of the L-function associated with a modular form is known to satisfy a functional equation, which may be even or odd. A result due to Gross and Zagier explicitly…
The Shafarevich conjecture for hypersurfaces in abelian varieties
Brian Lawrence, Will Sawin
Faltings proved that there are finitely many abelian varieties of genus over a number field , with good reduction outside a finite set of primes . Fixing one of these abe…
A counterexample to an optimistic guess about étale local systems
Brian Lawrence, Shizhang Li
In p-adic Hodge theory, it is known that if a Galois representation is de Rham, then it becomes semistable after extension of the base field. Liu and Zhu asked whether a correspond…
Two recent p-adic approaches towards the (effective) Mordell conjecture
Jennifer S. Balakrishnan, Alex J. Best, Francesca Bianchi +4
We give an introductory account of two recent approaches towards an effective proof of the Mordell conjecture, due to Lawrence--Venkatesh and Kim. The latter method, which is usual…