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- W2949667515 abstract "We show that an earlier conjecture of the author, on diophantine approximation of rational points on varieties, implies the ``abc conjecture'' of Masser and Oesterl'e. In fact, a weak form of the former conjecture is sufficient, involving an extra hypothesis that the variety and divisor admit a faithful group action of a certain type. Analogues of this weaker conjecture are proved in the split function field case of characteristic zero, and in the case of holomorphic curves (Nevanlinna theory). The proof of the latter involves a geometric generalization of the classical lemma on the logarithmic derivative, due to McQuillan. This lemma may be of independent interest." @default.
- W2949667515 created "2019-06-27" @default.
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- W2949667515 date "1999-08-06" @default.
- W2949667515 modified "2023-09-27" @default.
- W2949667515 title "On the abc conjecture and diophantine approximation by rational points" @default.
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