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 -conjecture to a restricted form. Such a reduction means that an effective -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}
}