English

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 SS-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 SS-unit equation is bounded uniformly in terms of #S\#S.

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