Inter-universal Teichmuller Theory I
------------------------------------
・Corrected 3 instances of a misprint in \S I4 ("Corollary 3.11" ---> "Theorem 3.11")
・Added a missing comma to the first line following the first display of Definition 4.1, (v)
・Slightly modified the phrasing ("profinite" ---> "topological") concerning profinite groups
in Definitions 4.1, (i); 6.1, (ii)
・Added a paragraph concerning "pseudo-monoids" and related notions to the beginning of \S 0
・Made various modifications concerning the Kummer theory of special types of rational functions,
as follows:
・Added Remark 3.1.7
・Rewrote Example 5.1, (i), (v); Remark 5.1.3; modified corresponding references to the content
of Example 5.1, (v), in the proof of Corollary 5.3, (i), and Example 5.4, (iv)
・Added Remark 5.1.4, together with a reference to this remark in Remark 6.12.3, (iii); added the paper
"Geometry of Anabelioids" (quoted in Remark 5.1.4) to the Bibliography
・Added items (v), (vi), (vii), (viii) to Definition 5.2; added a corresponding reference to
the proof of Corollary 5.3, (ii)
・Rewrote the latter portion of Example 5.4, (iv)
Inter-universal Teichmuller Theory II
-------------------------------------
・Added a supplementary explanation concerning mono-theta-theoretic cyclotomic rigidity (Remark 1.1.1),
together with a reference to this remark in the Introduction, as well as in Remarks 1.10.3; 4.11.4,
(iii), (b), and Corollary 3.6, (i)
・In Remark 1.10.3, added a reference to [IUTchIII], Remark 2.3.3
・Added a supplementary observation to the final portion of Remark 1.12.5, (ii)
・Added a missing "be" to the first sentence of Corollary 2.4, (i)
・Deleted an unnecessary comma (", and, moreover" ---> "and, moreover") following the first display
of Corollary 2.5, (iii); Remark 2.5.2, (ii); Corollary 2.8, (ii); Corollary 2.9, (ii), as well as
in Remark 4.7.4, (ii), (b)
・Corrected a misprint in Remark 2.8.3, (ii) (a missing "(-)")
・Added two missing "daggers" in the first line of the second display of Proposition 3.3
・In Proposition 4.1, (i) (respectively, 4.2, following the first display, and 4.2, (i); 4.3, (i); 4.4,
(i)), added a reference to [IUTchI], Definition, (v) (respectively, (vi); (vii); (viii))
・Slightly modified the titles of Corollaries 4.5, (v); 4.6, (v) ("Global Theta and Gaussian Monoids"
---> "Global Realified Theta and Gaussian Frobenioids")
・Rewrote Corollaries 4.7, 4.8 so as to take into account the modifications to [IUTchI] concerning
the Kummer theory of special types of rational functions; made a corresponding adjustment to the
wording of Remark 4.7.2, (b)
・Corrected a misprint in Remark 4.8.1, (ii) ("give rise" ---> "gives rise")
Inter-universal Teichmuller Theory III
--------------------------------------
・Made various modifications so as to take into account the modifications to [IUTchI] concerning
the Kummer theory of special types of rational functions as follows:
・Slightly modified the discussion of the first reference to [IUTchI], Example 5.1, (v), in the
Introduction
・Added an expanatory phrase ("at least in the usual naive sense") to Remark 1.5.2, (i), and modified
the initial portion of Remark 1.5.2, (ii)
・In Remark 2.1.1, (iv), added a reference to [IUTchII], Remark 1.1.1
・Rewrote Remark 2.2.2, (iii), and Fig. 2.3
・Added Remark 2.3.2, as well as references to Remark 2.3.2 in Remark 3.8.2; the final portion of
Theorem A, (i); the final portion of Theorem 3.11, (i)
・Added Remark 2.3.3
・Added Fig. 2.5
・Deleted Remarks 3.3.4, 3.7.1
・Deleted Remark 3.10.1; in Theorem A, (iii), and Remark 3.11.3, (ii), replaced references to
Remark 3.10.1 by references to Remark 2.3.2; in Remark 3.8.3, replaced a reference to Remark 3.10.1
by a reference to Theorem 3.11, (iii), (c), (d)
・Modified the first display of Theorem 3.11, (ii)
・Rewrote Theorem 3.11, (iii), (d)
・Modified the right-hand and lower left-hand portions of Fig. 3.4
・Modified the upper right-hand and lower central portions of Fig. 3.5
・Modified the final portion of Step (ii) of the proof of Corollary 3.12
・Rewrote various portions of Step (vi) of the proof of Corollary 3.12 related to Remarks 2.2.2, (iii);
2.3.2, 2.3.3
・Rewrote the latter portion of Remark 3.12.1, (iii), so as to take into account the content of
(the newly added) Remarks 2.3.2, 2.3.3
Inter-universal Teichmuller Theory IV
-------------------------------------
・Corrected 3 instances of a misprint in Remarks 3.6.1, (ii); 3.6.2, (i) ("Corollary 3.11" --->
"Theorem 3.11")
・In Remark 3.6.2, (i), replaced a reference to [IUTchIII], Remark 3.10.1, by a reference to
[IUTchIII], Remark 2.3.2
・In Remark 2.3.3, slighly modified the wording of the reference to [IUTchIII], Remark 3.12.1, (iii)