An effective Chabauty--Kim theorem

TY - JOUR

T1 - An effective Chabauty--Kim theorem

AU - Balakrishnan, Jennifer

AU - Dogra, Netan

PY - 2019/5/14

Y1 - 2019/5/14

N2 - The Chabauty–Kim method allows one to find rational points on curves under certain technical conditions, generalising Chabauty’s proof of the Mordell conjecture for curves with Mordell–Weil rank less than their genus. We show how the Chabauty–Kim method, when these technical conditions are satisfied in depth 2, may be applied to bound the number of rational points on a curve of higher rank. This provides a non-abelian generalisation of Coleman’s effective Chabauty theorem.

AB - The Chabauty–Kim method allows one to find rational points on curves under certain technical conditions, generalising Chabauty’s proof of the Mordell conjecture for curves with Mordell–Weil rank less than their genus. We show how the Chabauty–Kim method, when these technical conditions are satisfied in depth 2, may be applied to bound the number of rational points on a curve of higher rank. This provides a non-abelian generalisation of Coleman’s effective Chabauty theorem.

UR - https://arxiv.org/abs/1803.10102

U2 - 10.1112/S0010437X19007243

DO - 10.1112/S0010437X19007243

M3 - Article

SN - 0010-437X

VL - 155

SP - 1057

EP - 1075

JO - COMPOSITIO MATHEMATICA

JF - COMPOSITIO MATHEMATICA

IS - 6

ER -