21/08/26 09:43:54.81 dl10YEoF.net
メモ（math jin より）
これは、何を証明しているのでしょうか？
URLﾘﾝｸ(arxiv.org)
[Submitted on 15 Oct 2020]
Two Restricted ABC Conjectures
Machiel van Frankenhuijsen
Ellenberg proved that the abc conjecture would follow if this conjecture were known for sums a+b=c such that D?abc for some integer~D. Mochizuki proved a theorem with an opposite restriction, that the full abc conjecture would follow if it were known for abc sums that are not highly divisible. We prove both theorems for general number fields.
Comments: 22 pages
URLﾘﾝｸ(arxiv.org)
Abstract. Ellenberg proved that the abc conjecture would follow if this conjecture were known for sums a + b = c such that
D | abc for some integer D. Mochizuki proved a theorem with an
opposite restriction, that the full abc conjecture would follow if it
were known for abc sums that are not highly divisible. We prove
both theorems for general number fields.
1.1. Acknowledgements. In [1], Ellenberg mentions that his result
was known to the experts, and he cites [7]. We call it Ellenberg’s
theorem, but it should probably be attributed to Szpiro and Oesterl´e.
We thank Mochizuki for many insightful discussions, and the Research Institute for Mathematical Sciences of the University of Kyoto
for their hospitality from January until August of 2018.