• Corpus ID: 53056622

Why abc is still a conjecture

@inproceedings{Scholze2018WhyAI,
  title={Why abc is still a conjecture},
  author={Peter Scholze},
  year={2018}
}
In March 2018, the authors spent a week in Kyoto at RIMS of intense and constructive discussions with Prof. Mochizuki and Prof. Hoshi about the suggested proof of the abc conjecture. We thank our hosts for their hospitality and generosity which made this week very special. We, the authors of this note, came to the conclusion that there is no proof. We are going to explain where, in our opinion, the suggested proof has a problem, a problem so severe that in our opinion small modifications will… 
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References

SHOWING 1-9 OF 9 REFERENCES
ARITHMETIC ELLIPTIC CURVES IN GENERAL POSITION
We combine various well-known techniques from the theory of heights, the theory of “noncritical Belyi maps”, and classical analytic number theory to conclude that the “ABC Conjecture”, or,
THE GEOMETRY OF FROBENIOIDS II: POLY-FROBENIOIDS
We develop the theory of Frobenioids associated to non-archimedean (mixed-characteristic) and archimedean local fields. Inparticular, we show that the resulting Frobenioids satisfy the properties
TOPICS IN ABSOLUTE ANABELIAN GEOMETRY III: GLOBAL RECONSTRUCTION ALGORITHMS
In the present paper, which forms the third part of a three-part series on an algorithmic approach to absolute anabelian geometry, we apply the ab- solute anabelian technique of Belyi cuspidalization
Heights in Diophantine Geometry
I. Heights II. Weil heights III. Linear tori IV. Small points V. The unit equation VI. Roth's theorem VII. The subspace theorem VIII. Abelian varieties IX. Neron-Tate heights X. The Mordell-Weil
THE GEOMETRY OF FROBENIOIDS I: THE GENERAL THEORY
We develop the theory of Frobenioids, which may be regarded as a category-theoretic abstraction of the theory of divisors and line bundles on models of finite separable extensions of a given function
Non-critical Belyi maps
  • Math. J. Okayama Univ
  • 2004
6-8, 60325 Frankfurt am Main, Germany E-mail address: stix@math.uni-frankfurt
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The Geometry of Frobenioids II