TY - JOUR
T1 - Bounds on the Chabauty–Kim Locus of Hyperbolic Curves
AU - Betts, L. Alexander
AU - Corwin, David
AU - Leonhardt, Marius
N1 - Publisher Copyright:
© The Author(s) 2024. Published by Oxford University Press. All rights reserved.
PY - 2024/6/1
Y1 - 2024/6/1
N2 - Conditionally on the Tate–Shafarevich and Bloch–Kato Conjectures, we give an explicit upper bound on the size of the p-adic Chabauty–Kim locus, and hence on the number of rational points, of a smooth projective curve X/Q of genus g ≥ 2 in terms of p, g, the Mordell–Weil rank r of its Jacobian, and the reduction types of X at bad primes. This is achieved using the effective Chabauty–Kim method, generalizing bounds found by Coleman and Balakrishnan–Dogra using the abelian and quadratic Chabauty methods.
AB - Conditionally on the Tate–Shafarevich and Bloch–Kato Conjectures, we give an explicit upper bound on the size of the p-adic Chabauty–Kim locus, and hence on the number of rational points, of a smooth projective curve X/Q of genus g ≥ 2 in terms of p, g, the Mordell–Weil rank r of its Jacobian, and the reduction types of X at bad primes. This is achieved using the effective Chabauty–Kim method, generalizing bounds found by Coleman and Balakrishnan–Dogra using the abelian and quadratic Chabauty methods.
UR - http://www.scopus.com/inward/record.url?scp=85196758386&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnae067
DO - 10.1093/imrn/rnae067
M3 - Article
AN - SCOPUS:85196758386
SN - 1073-7928
VL - 2024
SP - 9705
EP - 9727
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 12
ER -