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(引用開始)
【RIMS-1758】
Shinichi MOCHIZUKI
INTER-UNIVERSAL TEICHM\"{U}LLER THEORY III: CANONICAL SPLITTINGS OF THE LOG-THETA-LATTICE
August , 2012
[RIMS1758.ps.gz] [RIMS1758.pdf]
(引用終り)
IUT III Corollary 3.12の証明 2012年版 を、スナップショットしておく
P113～121まで、約8頁ある
（参考）
URLﾘﾝｸ(www.kurims.kyoto-u.ac.jp)
RIMS-1758
INTER-UNIVERSAL TEICHMULLER THEORY III: ¨
CANONICAL SPLITTINGS OF THE LOG-THETA-LATTICE
By Shinichi MOCHIZUKI
August 2012
P113
Corollary 3.12. (Log-volume Estimates for Θ-Pilot Objects) Suppose
that we are in the situation of Theorem 3.11. Write
? |log(Θ)| ∈ R ∪{+∞}
for the procession-normalized mono-analytic log-volume
Proof. Suppose that we are in the situation of Theorem 3.11. We begin by
reviewing precisely what is achieved by the various portions of Theorem 3.11 and,
indeed, by the theory developed thus far in the present series of papers. This review
leads naturally to an interpretation of the theory that gives rise to the inequality
asserted in the statement of Corollary 3.12. For ease of reference, we divide our
discussion into steps, as follows.
P121
Put another way, one must contend with the indeterminacy
arising from the fact that, unlike the case with the global Frobenioids “F◎_MOD”,
“F◎R_MOD”, objects of the various local Frobenioids that arise admit endomorphisms
which are not automorphisms. This indeterminacy has the effect of rendering
meaningless any attempt to perform a precise log-volume computation as in (xi).