On the $abc$ conjecture

Using adelic intersection theory and following the method envisioned by Parshin and Moret-Bailly, we prove a conjecture of Vojta for curves of genus two and a weak form of the $abc$ conjecture

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-03
DOI
https://doi.org/10.48550/arxiv.2611.05217
Primary Topic
Algebraic Geometry and Number Theory
Type
preprint
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preprint

On the $abc$ conjecture

Christophe Soulé
arXiv (Cornell University)
Algebraic Geometry and Number Theory
preprint

On the $abc$ conjecture

Christophe Soulé
preprint en

Abstract

Using adelic intersection theory and following the method envisioned by Parshin and Moret-Bailly, we prove a conjecture of Vojta for curves of genus two and a weak form of the $abc$ conjecture

arXiv (Cornell University)
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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On the $abc$ conjecture — Christophe Soulé · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS