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arxiv: 1601.03572 · v1 · pith:AGQWBXHMnew · submitted 2016-01-14 · 🧮 math.NT

Effectivity in Mochizuki's work on the abc-conjecture

classification 🧮 math.NT
keywords mochizukiconjecturetheoremarithmeticbelyicomputablecomputationsconstructive
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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 $abc$-conjecture to a restricted form. Such a reduction means that an effective $abc$-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").

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