English

Effectivity in Mochizuki's work on the $abc$-conjecture

Number Theory 2016-01-15 v1

Abstract

This note outlines a constructive proof of a proposition in Mochizuki's paper "Arithmetic elliptic curves in general position," making a direct use of computable non-critical Belyi maps to effectively reduce the full abcabc-conjecture to a restricted form. Such a reduction means that an effective abcabc-theorem is implied by Theorem 1.10 of Mochizuki's final IUT paper ("Inter-universal Teichmuller theory IV: log-volume computations and set-theoretic foundations").

Keywords

Cite

@article{arxiv.1601.03572,
  title  = {Effectivity in Mochizuki's work on the $abc$-conjecture},
  author = {Vesselin Dimitrov},
  journal= {arXiv preprint arXiv:1601.03572},
  year   = {2016}
}
R2 v1 2026-06-22T12:29:23.172Z