Weight filtrations on Selmer schemes and the effective Chabauty--Kim method
Number Theory
2021-06-03 v1
Abstract
We develop an effective version of the Chabauty--Kim method which gives explicit upper bounds on the number of -integral points on a hyperbolic curve in terms of dimensions of certain Bloch--Kato Selmer groups. Using this, we give a new "motivic" proof that the number of solutions to the -unit equation is bounded uniformly in terms of .
Keywords
Cite
@article{arxiv.2106.01218,
title = {Weight filtrations on Selmer schemes and the effective Chabauty--Kim method},
author = {L. Alexander Betts},
journal= {arXiv preprint arXiv:2106.01218},
year = {2021}
}
Comments
74 pages, comments welcome