Inter-universal Teichmuller Theory I
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・Updated the Acknowledgements
・Added a reference to Remark 3.4.3, (i), in Remark 3.1.2, (ii)
・In Remark 3.1.7, (i), slightly simplified the definition of a "\kappa-coric function" in the archimedean case
and added a reference to Definition 5.2, (viii)
・In Example 3.4, (i), added references to Remark 3.4.3, (i), and [AbsTopIII], Definition 2.1, (i)
・Added Remark 3.4.3
・Slightly modified the discussion immediately following the third display of Definition 5.2, (vii), so as to
take into account Remarks 2.5.3, (i); 3.4.3, (ii)
・Rewrote the portion of Definition 5.2, (viii), following the second display
・Slightly modified the portion concerning the archimedean case of the discussion immediately following the
fourth display of Example 5.4, (iv)
Inter-universal Teichmuller Theory II
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・Updated the Acknowledgements
・In the statement of Proposition 4.2, (i), slightly modified the reference to [IUTchI], Definition 5.2, (vi)
・Corrected a misprint ("Coric Realified Global" ---> "Coric Global Realified") in the title of the statement of Corollary 4.10, (v)
Inter-universal Teichmuller Theory III
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・Slightly modified the phrasing in the Introduction ("various versions" ---> "various versions of the notion of a log-shell")
・In the Introduction, added a reference to [AbsTopIII], \S I1
・In the Introduction, slightly modified one of the references to Remark 1.2.2 ("Remark 1.2.2" ---> "Remark 1.2.2, (iii)")
・In the Introduction, slightly modified the phrasing concerning vertically coric log-shells
・In the Introduction, slightly modified the phrasing concerning the theory of [IUTchII], \S 4 ("not addressed in the theory of [IUTchII], \S 4"
---> "not explicitly addressed in [IUTchII], \S 4")
・Replaced "appropriate" by "suitable" (4 instances: Introduction; Remark 1.5.3, (i); Remark 2.2.1, (ii); Proposition 3.4, (i))
・Slightly modified the description of "(Ind2)" given in the Introduction and the statement of Theorem A, (i)
・In the Introduction, corrected a misprint ("with the local integers ... with the local units" ---> "with the local units") in the discussion
concerning non-interference properties; slightly modified the phrasing of the subsequent discussion of canonical splittings
・In the Introduction, slightly modified the phrasing concerning Kummer theory ("Kummer theory concerning" ---> "Kummer theory surrounding")
・Corrected misprints ("realified global" ---> "global realified", 11 instances) in the Introduction (2 instances); the statement of Theorem 1.5,
(iii); Remark 1.5.2, (i), (iii); Remark 1.5.3, (iii) (3 instances); Proposition 3.7, (iii) (2 instances), (iv)
・In the Introduction, removed the parentheses and slightly modified the phrasing surrounding mention of the "holomorphic hull" (4 instances)
・Slightly modified the discussion of "a somewhat intricate intertwining" in the final portion of the Introduction and added a reference to
Remark 3.12.2, (ii)
・In the final portion of the Introduction, slightly modified the discussion of the indeterminacies (Ind1), (Ind2), (Ind3)
・Slightly modified the phrasing in the final portions of the statements of Theorem B and Corollary 3.12, as well as related phrasing in
Step (xi) of the proof of Corollary 3.12
・Updated the Acknowledgements
・In Remark 1.4.1, (ii), added a reference to Remark 1.2.2, (iii)
・Slightly modified the reference to "Remark 3.6.2, (i)" in the statement of Proposition 2.1, (iii)
・Added items (iii) and (iv) to Remark 3.1.1, as well as references to these items in the statements of Theorem B; Proposition 3.9, (i);
Theorem 3.12
・At the beginning of the statement of Proposition 3.2, (ii), added a supplementary explanatory phrase concerning the word "determine"
・Added missing "log(-)"'s (2 instances) in the final sentence of statement of Proposition 3.4, (i)
・Corrected a misprint ("appear in such a procession" ---> "appears in such a procession") in the statement of Proposition 3.4, (ii)
・Slightly modified the text surrounding the second display of the statement of Proposition 3.4, (ii)
・Slightly modified the text immediately following the second and fourth displays of the statement of Proposition 3.5, (i)
・Added an explanatory phrase concerning the case "j=0" at the beginning of statement of Proposition 3.5, (ii), (a), (b)
・Added a reference to Remark 3.11.4 in the statement of Propositions 3.5, (ii); 3.10, (ii)
・Slightly modified the reference to [IUTchIV] ("[IUTchIV]" ---> "[IUTchIV], \S 1") in Remark 3.9.1, (iii)
・Slightly modified the definition of a "holomorphic hull" in Remark 3.9.5
・Slightly modified the notation in the explanation immediately following the first display of the statement of Proposition 3.10, (ii)
・Slightly modified the discussion immediately following the third display of the statement of Proposition 3.10, (ii)
・Corrected a misprint ("cf. the natural isomorphisms" ---> "cf. the natural poly-isomorphisms") in the statement of Theorem 3.11, (i), (c)
・At the beginning of the statement of Theorem 3.11, (ii), added a supplementary explanatory phrase concerning the indeterminacies (Ind1), (Ind2)
・Corrected a misprint ("non-realified/realified global" ---> "global non-realified/realified") in the statement of Theorem (ii), (c)
・In the proof of Theorem 3.11, added references to Remarks 3.11.3, 3.11.4
・Slightly modified the phrasing of the final sentence of Remark 3.11.2, (iv)
・Slightly modified the phrasing in the final display of Remark 3.11.3, (ii), as well as in Remark 3.11.3, (iv)
・Corrected a misprint ("pre-composition of" ---> "pre-composition with") in Remark 3.11.3, (iii)
・In Remark 3.11.4, (i), italicized certain phrases and slightly modified the discussion surrounding the second display
・Slightly modified the phrasing of Step (ii) and Fig. 3.6 of the proof of Corollary 3.12
・In Step (vi) of the prooof of Corollary 3.12, slightly modified the phrasing as the end of the first display, as well as the discussion
following the second display
・Slightly modified the phrasing of the final sentence of Step (vii) of the proof of Corollary 3.12
・In Step (xi) of the proof of Corollary 3.12, added references to Remarks 3.9.2; 3.12.2, (ii), and slightly modified the phrasing of the
discussion of holomorphic hulls
・Slightly modified the phrasing of the second sentence of Remark 3.12.1, (iii)
・Corrected a misprint ("follows." ---> "follows:") in Remark 3.12.2, (i)
・Rewrote Remark 3.12.2, (ii)
・In Remark 3.12.2, (v), slightly modified the phrasing near the beginning ("treated with regard to" ---> "treated in their relationship to")
and added a reference to Remark 3.6.2, (i)
・Slightly modified the phrasing ("volume distortion" ---> "conformality distortion") in the display of Remark 3.12.3, (ii)
・Slightly modified various portions of Fig. 3.10 (e.g., the portion concerning the indeterminacies (Ind1), (Ind2), (Ind3))
・Added "[Royden]" to the Bibliography