English

On Smirnov's approach to the ABC conjecture

Number Theory 2024-01-17 v2 Algebraic Geometry

Abstract

We use algebraic geometry over pointed monoids to give an intrinsic interpretation for the compactification of the spectrum of the ring of integers of a number field KK, for the projective line over algebraic extensions of F1\mathbb{F}_1 and for maps between them induced by elements of KK, as introduced by Alexander Smirnov in his approach to the ABC conjecture.

Keywords

Cite

@article{arxiv.2306.16637,
  title  = {On Smirnov's approach to the ABC conjecture},
  author = {Manoel Jarra},
  journal= {arXiv preprint arXiv:2306.16637},
  year   = {2024}
}

Comments

13 pages, minor corrections. arXiv admin note: text overlap with arXiv:2305.15953