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２）
Corollary 2.3. (Diophantine Inequalities) と、Theorem A. (Diophantine Inequalities) は、ほぼ同じか

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Corollary 2.3. (Diophantine Inequalities)

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Remark 2.3.1. We take this opportunity to correct some unfortunate misprints
in [GenEll].

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Remark 2.3.4. Various aspects of the theory of the present series of papers
are substantially reminiscent of the theory surrounding Bogomolov’s proof of
the geometric version of the Szpiro Conjecture, as discussed in [ABKP], [Zh].
Put another way, these aspects of the theory of the present series of papers may
be thought of as arithmetic analogues of the geometric theory surrounding Bogomolov’s proof. Alternatively, Bogomolov’s proof may be thought of as a sort of
useful elementary guide, or blueprint [perhaps even a sort of Rosetta stone!],
for understanding substantial portions of the theory of the present series of papers.
The author would like to express his gratitude to Ivan Fesenko for bringing to his
attention, via numerous discussions in person, e-mails, and skype conversations
between December 2014 and January 2015, the possibility of the existence of such
fascinating connections between Bogomolov’s proof and the theory of the present
series of papers. We discuss these analogies in more detail in [BogIUT].

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