ΔΑ͏Ͱ͕͢ɺʮຊ໋ʯͱͯ͠ೝࣝ͞ΕΔ΂͖΋ͷ͸ʮIUTeichཧ࿦ʯͱ ͍͏ཧ࿦ͷํͰ͋Γɺཧ࿦ͱൺֱ͢Δͱɺෆ౳ࣜ͸ཧ࿦͕೗Կʹਂ͍ͱ͜ Ζ·Ͱ۷ΓԼ͍͛ͯΔ΋ͷͰ͋Δ͔Λࣔ͢୯ͳΔʮҰͭͷࢦඪʯʹա͗· ͤΜɻ ɾҰ࣌ؒߨԋͲ͜Ζ͔ɺҰिؒఔ౓ͷղઆͰ΋ɺཧ࿦ͷେ·͔ͳ࢓૊ΈΛຊ ֨తʹೲಘͰ͖ΔΑ͏ͳܗͰཧղ͢Δ͜ͱ͸ଟ͘ͷݚڀऀͷ৔߹ɺࠔ೉Ͱ ͋ΓɺͦͷΑ͏ͳ୹ظؒͷ޿ใ׆ಈʹՌͨͯ͠ҙຯ͕͋Δ͔Ͳ͏͔ɺ͜Ε ·ͰͷܦݧΛৼΓฦΔͱɺେ͍ʹٙ໰͕͋ΔΑ͏ʹײ͡·͢ɻҰํɺݸਓ ͕ࠩ͋Δͱ͸͍͑ɺ

ژ౎େֶ਺ཧղੳݚڀॴɾڭतɹ๬݄৽Ұ

ɹ2012೥8݄຤ʹӉ஦ࡍλΠώϛϡʔϥʔཧ࿦ʢIUTeichʣʹؔ͢Δ࿈ଓ࿦จΛൃ

ද͔ͯ͠Β 1೥ 4ϲ݄ఔܦա͓ͯ͠Γ·͕͢ɺͦͷؒɺཧ࿦ͷݕূΛ८༷ͬͯʑͳ ಈ͖͕͋Γ·ͨ͠ͷͰ͝ใࠂ͠·͢ɻ

(1) 2012೥8 ݄຤ʹ IUTeichཧ࿦ʹؔ͢Δ࿈ଓ࿦จʢ4รʣΛϓϨϓϦϯτͱͯ͠

ൃද͠ɺֶज़ࡶࢽʹ౤ߘ͠·ͨ͠ɻ౤ߘઌͷࡶࢽ໊΋ɺͦͷଞɺ౤ߘʹؔ͢Δ৘ใ

͸ެ։͓ͯ͠Γ·ͤΜɻ࿦จͷެ։ͷ໨త͸͋͘·Ͱ΋ઐ໳ՈʹΑΔֶ໰తݕূͰ

͋ΓɺҰൠࣾձ޲͚ͷൃදͰ͸͋Γ·ͤΜɻͳ͓ɺඇઐ໳ՈʹΑΔඇֶ໰తͳ಺༰ ͷ൓Ԡ͸࠷ॳ͔Βશ͘૝ఆ͓ͯ͠Γ·ͤΜ͠ɺͦͷΑ͏ͳಈ͖ʹରͯ͠͸ݪଇͱ͠

ͯରԠ͠ͳ͍͜ͱʹ͓ͯ͠Γ·͢ɻ

(2) IUTeichཧ࿦ͷޱ಄ൃද͸ݱࡏͷͱ͜Ζɺژ౎େֶͰ͸

2010೥10݄ʢʹʮ༧ࠂรʯɺ1࣌ؒʣͱ 2012೥12݄ʢ1 ࣌ؒʣ

ͷ2 ճɺ౦ژେֶͰ͸

2013೥6 ݄ʢ1࣌ؒ൒ʣ

ͷ1ճɺߦͳ͓ͬͯΓ·͢ɻߨԋͷεϥΠυ͸ࢲͷ΢ΣϒαΠτʢʹʮग़ுɾߨԋʯ ͱ͍͏ทʣͰެ։͓ͯ͠Γ·͢ɻ2014೥΋ɺগͳ͘ͱ΋1 ճɺ೔ຊࠃ಺ͷେֶʹ͓

͍ͯߨԋΛߦͳ͏ํ޲Ͱߟ͓͑ͯΓ·͢ɻͲͷߨԋ΋಺༰͸ຆͲมΘ͓ͬͯΒͣɺ

ͦͷ಺༰ʹ͍ͭͯ͸αʔϕΠ [Pano] ʹ͓͍ͯΑΓৄࡉʹղઆ͓ͯ͠Γ·͢ɻ͜ͷ αʔϕΠ͸ࢲͷ΢ΣϒαΠτͷʮ࿦จʯͱ͍͏ทͰެ։͓ͯ͠Γɺ·ͨ 2012೥12

݄ͷߨԋΛߦͳͬͨݚڀूձͷใࠂूʹऩ࿥͞ΕΔ༧ఆͰ͢ɻ

(3) ࢁԼ߶ࢯʢ๛ాதԝݚڀॴ٬һݚڀһɾژ౎େֶ਺ཧղੳݚڀॴ਺ཧղੳݚڀ

ަྲྀηϯλʔಛ೚ߨࢣʣ͸

2012೥10݄Ҏ߱ɺ݄1ճʢʹ 2೔ؒ ≈ ໿12࣌ؒʣ

ࢲͱೋਓͰߦͳ͍ͬͯΔηϛφʔʹ͓͍ͯཧ࿦ͷݕূΛਐΊ͍ͯ·͢ɻ۩ମతʹ͸ɺ 2012೥10݄ʙ12݄ͷؒ

͸ʮ४උͷ࿦จʯʢʹ[HASurI], [HASurII], [SemiAnbd], [FrdI], [FrdII], [EtTh], [Ab-

sTopIII], [GenEll]౳ʣΛษڧ͠ɺͦͷ಺༰ʹ͍ͭͯηϛφʔͰৄٞ͘͠࿦͠·ͨ͠ɻ

ͦͷޙɺࢁԼࢯ͸

2013೥1 ݄ʙ2013೥3݄ɺ͓Αͼ 2013೥4 ݄ʙ2013೥9݄

ͷ2ճʹΘͨΓɺཧ࿦ͷʮຊମʯͰ͋Δ[IUTchI], [IUTchII], [IUTchIII], [IUTchIV]

ͷ 4รͷ࿦จΛ࠷ޙ·ͰಡΈऴ͍͑ͯ·͢ɻ͜ͷ໿ 1೥ͷؒʹɺʮ४උͷ࿦จʯͱ ʮຊମʯʹ͍ͭͯɺ௨ৗͷֶज़ࡶࢽͷࠪಡΛང͔ʹ௒͑ΔΑ͏ͳৄࡉͳٕज़తͳࢦఠ ʢʹ1೥༨ΓͰ਺ඦ݅ఔ౓ʂʣΛࢲ͸ࢁԼࢯΑΓॻ໘ʢʹిࢠϝʔϧʣͰ͍͍ͨͩͯ

͓Γ·͢ɻͦͷ๲େͳ਺ͷࢦఠʹ͍ͭͯ͸ɺηϛφʔͰٞ࿦ͨ͠ޙɺ֘౰͢Δ࿦จ Λमਖ਼͠ɺࢲͷ΢ΣϒαΠτͷʮ࿦จʯͱ͍͏ทͰमਖ਼൛Λެ։͓ͯ͠Γ·͢ɻ·

ͨ 2013೥ 4 ݄ࠒɺࢁԼࢯ͸ݚڀूձ౳ͰͷަྲྀΛ௨ͯ͡ଞͷݚڀऀ͔ΒدͤΒΕ

࣭ͨ໰ʹରԠ͢ΔͨΊɺIUTeichཧ࿦ʹؔ͢ΔʮFAQʯΛ࡞੒͠ɺࢲͷ΢ΣϒαΠ τͰެ։͠·ͨ͠ɻ͜ͷ2 ճʹΘͨΔ࿦จͷӾಡʹΑΓࢁԼࢯ͸ཧ࿦Λৄ͘͠ཧղ

͠ɺͦͷਖ਼͠͞ΛҰ௨Γ֬ೝ͍ͯ͠·͕͢ɺ͜ͷ࿦จͷӾಡ͸ࢁԼࢯʹͱͬͯ͸୯ ͳΔʮγϯάϧɾνΣοΫʯʢຊਓͷݴ༿ʣʹա͗·ͤΜɻɹ

(4) ࢁԼࢯ͸ɺIUTeichཧ࿦ͷʮμϒϧɾνΣοΫʯʢຊਓͷݴ༿ʣͱͯ͠

2013೥5݄ʙ2013೥11݄ͷؒɺ݄1 ճʢʹ2ʙ3೔ؒ ≈ 16ʙ24࣌ؒʣ

࣍ͷࡾਓ

ۄ઒ٍ҆உࢯʢژ౎େֶ਺ཧղੳݚڀॴɾڭतʣ

੕༟Ұ࿠ࢯʢژ౎େֶ਺ཧղੳݚڀॴɾߨࢣʣ

দຊᚸࢯʢ޿ౡେֶେֶӃཧֶݚڀՊ਺ֶઐ߈ɾڭतʣ

Λର৅ʹɺIUTeichཧ࿦Λղઆ͢ΔηϛφʔΛߦͳ͍·ͨ͠ɻࢲΛࢀՃऀ͔Β֎͠

ͨܗͰηϛφʔ͕ߦͳΘΕ·͕ͨ͠ɺ͜Ε͸ࢁԼࢯ͕ཧ࿦Λࣗ෼ͷݴ༿Ͱઆ໌͠ɺ

ࣗ෼ͷཧղΛ֬ೝ͢ΔػձͱͳΔΑ͏ʹͱΒΕͨાஔͰ͢ɻηϛφʔ͸ʮ४උͷ࿦

จʯͷॳาతͳ෦෼͔Βʮຊମʯͷ࠷ޙ·Ͱɺ࿦จͷʮఆٛʯ΍ʮ໋୊ʯɺʮఆཧʯ

౳ΛҰݸͣͭॱ൪ʹղઆ͍ͯ͘͠ͱ͍͏ɺߨࢣ͓ΑͼࢀՃऀશһͷେมͳ࿑ྗΛඞ ཁͱ͢ΔܗࣜͰਐΊΒΕ·ͨ͠ɻηϛφʔத͓Αͼͦͷ४උͷաఔͰٕज़తͳࢦఠ

΍ٙ໰౳͕ൃੜͨ͠ͱ͖ʢʹฏۉతʹ͸݄ʹ10ʙ30݅ఔ౓ʣ͸ɺཌ݄ͷࢲͱͷηϛ φʔͰٞ࿦͠ɺॲཧ͠·ͨ͠ɻʢμϒϧɾνΣοΫͷʣηϛφʔ͕ऴྃͨ͠ࠒʹ͸ࢀ

Ճऀ͔ΒɺফԽʹ͸·ֻ͕͔ͩ࣌ؒΓͦ͏͕ͩɺཧ࿦ͷུ֓͸Ұ௨ΓཧղͰ͖ͨझ ࢫͷൃݴ͕ฉ͔Ε·ͨ͠ɻ·ͨɺཧ࿦ΛҰ௨Γษڧ͠ऴཱ͑ͨ৔͔ΒվΊͯݕূ͠

ͨͱ͜Ζɺ(2)Ͱݴٴͨ͠ߨԋ΍αʔϕΠͷ಺༰͸ʮద੾ʯͰ͋ΔͱͷධՁΛࢀՃऀ

͔Β͍͖ͨͩ·ͨ͠ɻ

(5) ࢁԼࢯ͸੒ޭཪʹऴྃͨ͠(4)ͷʮμϒϧɾνΣοΫʯ͚ͩͰ͸๞͖଍Γͣɺʮτ ϦϓϧɾνΣοΫʯʢຊਓͷݴ༿ʣͱͯ͠ɺIUTeichཧ࿦ͷৄࡉͳղઆΛ໨తͱ͢Δ

αʔϕΠͷࣥචΛ։͍࢝ͯ͠·͢ɻ͜ͷαʔϕΠ͸ 200ʙ300 ทఔͷ௕͞ʹͳΔݟ ௨͠Ͱ͋Δͱͷ͜ͱͰ͢ɻ·ͨɺ೔ఔ౳͸·ͩ֬ఆ͍ͯ͠ͳ͍΋ͷͷɺ2014೥4݄ Ҏ߱ɺ۝भେֶͷాޱ༤Ұ࿠।ڭतͷґཔͰ۝भେֶʹ͓͍ͯIUTeichཧ࿦Λղઆ

͢Δʢ਺िؒఔ౓ͷʣूதߨٛΛߦͳ͏ํ޲Ͱݕ౼͍ͯ͠ΔΑ͏Ͱ͢ɻ

(6) Mohamed Sa¨ıdiࢯʢΤΫηλʔେֶʢ࿈߹Ԧࠃʣɾ।ڭतʣ͸

2013೥7 ݄ʙ9݄ͷ 3ϲ݄ؒɺ

٬һڭतͱͯ͠ژ౎େֶ਺ཧղੳݚڀॴʹ଺ࡏ͠ɺ଺ࡏظؒதɺ 10ճఔʢ≈ ܭ24࣌ؒఔ౓ʣ

ߦͳͬͨηϛφʔʹ͓͍ͯIUTeichཧ࿦ʹ͍ͭͯࢲͱೋਓͰٞ࿦͠ɺ༷ʑͳ؍఺͔

Βݕূ͠·ͨ͠ɻ·ͨࢁԼࢯͱ΋਺ճఔηϛφʔΛߦͳ͍ɺIUTeichཧ࿦ʹ͍ͭͯ

ٞ࿦͠·ͨ͠ɻSa¨ıdiࢯ͸଺ࡏ͢Δલͷ൒೥༨Γͷؒɺʮ४උͷ࿦จʯͱɺͦΕ͔Β ʮຊମʯͷ൒෼ఔ౓ΛಡΈऴ͑ͨΒ͘͠ɺདྷ೔͞Ε͔ͯΒ͸ʮຊମʯͷ࢒Γͷ൒෼Λ ಡΈऴ͑ɺ·ͨ೦ͷͨΊͷ֬ೝͱͯ͠ɺʮຊମʯΛվΊͯ࠷ॳ͔Β࠷ޙ·ͰಡΈ௚͠

ͨͦ͏Ͱ͢ɻ͜ͷ2ճͷӾಡΛߦͳ͍ͬͯͨؒɺSa¨ıdiࢯ͸΄΅ि̍ճͷηϛφʔͰ

࿦จͷ಺༰ʹ͍ͭͯࢲͱపఈతʹٞ࿦Λ͠ɺ·ͨ௨ৗͷֶज़ࡶࢽͷࠪಡΛང͔ʹ௒

͑ΔΑ͏ͳৄࡉͳٕज़తͳࢦఠʢʹ3ϲ݄ఔ౓Ͱඦ݅લޙʂʣΛͯ͠Լ͍͞·ͨ͠ɻ

ࢁԼࢯͷͱ͖ͱಉ༷ɺࢲ͸͍͍ͨͩͨࢦఠʹ͍ͭͯɺηϛφʔͰٞ࿦ͨ͠ޙɺ֘౰

͢Δ࿦จΛमਖ਼͠ɺࢲͷ΢ΣϒαΠτͷʮ࿦จʯͱ͍͏ทͰमਖ਼൛Λެ։͓ͯ͠Γ

·͢ɻ͜ΕΒͷ׆ಈΛܦͯ Sa¨ıdiࢯ͸ཧ࿦͕ਖ਼͍͠ͱͷݟղΛࢲࣗ਎ʹରͯ͠΋ւ

֎ͷୈࡾऀʹରͯ͠΋ड़΂͍ͯ·͢ɻɹ

(7) ࢁԼࢯͱ Sa¨ıdi ࢯ͸ಉ͡਺࿦زԿͱ͍͏ઐ໳෼໺ͷݚڀऀͱ͸͍͑ɺաڈͷ࿦

จ౳ͷ࢓ࣄΛৼΓฦΔͱ໌Β͔ͳΑ͏ʹɺ਺ֶతͳഎܠ͕͍ͩͿҧ͏ೋਓͰ͋Δ͜

ͱ΋ࣄ࣮Ͱ͢ɻ͔͜͠͠ͷೋਓͷҰͭͷॏཁͳڞ௨఺ͱͯ͠ɺ͜Ε·Ͱଟ਺ͷ਺࿦

زԿͷ࿦จʹֶ͍ͭͯज़ࡶࢽͷґཔͰࠪಡΛ͠ɺܝࡌద౰ͷՄ൱Λ൑அ͢ΔܦݧΛ

͍࣋ͬͯΔͱ͍͏ɺࠪಡऀͱͯ͠ͷ๛෋ͳ࣮੷͕ڍ͛ΒΕ·͢ɻҰํɺཧ࿦ͷॏཁ

ੑ΍ख๏ͷ৽حੑΛߟྀ͢Δͱɺ৻ॏͳ࢟੎͕ٻΊΒΕΔঢ়گͰ͋Γɺ͜ͷೋਓʹ ΑΔ͜Ε·ͰͷIUTeichཧ࿦ͷݕূΛ΋ͬͯཧ࿦ͷݕূ͕ࣄ্࣮׬ྃͨ͠ͱߟ͑Δ

΂͖͔Ͳ͏͔ɺେ͍ʹٞ࿦ͷ༨஍͕͋Γɺʮ࠷ऴతͳ݁࿦ʯΛग़͢͜ͱ͸ࠓճͷใࠂ ͷൣғΛ௒͍͑ͯΔͱݴΘ͟ΔΛಘ·ͤΜɻ͔͠͠ೋਓͷࠪಡऀͱͯ͠ͷ࣮੷Λ౿

·͑ͯߟ͑Δͱɺ(3), (4), (6)Ͱใࠂͨ͜͠Ε·Ͱͷݕূ׆ಈ͸طʹͦͷʮ໖ີ͞ʯ

͓Αͼʮղ૾౓ʯʹ͓͍ͯҰൠతͳ਺ֶ࿦จͷࠪಡͷൣғΛେ෯ʹ௒͓͑ͯΓɺͦ

ͷ׆ಈΛ௨ͯ͠ೋਓ͔Β͍͍͍ͨͩͯΔIUTeichཧ࿦ʹର͢ΔۃΊͯߠఆతͳධՁ ʹ͸ҰఆͷॏΈ͕͋Δͱߟ͓͑ͯΓ·͢ɻ

(8) ࢁԼࢯͱSa¨ıdiࢯʹΑΔIUTeichཧ࿦ͷݕূ׆ಈͷ΋͏Ұͭͷॏཁͳʮऩ֭ʯ͸ɺ

਺ֶతഎܠ͕େ͖͘ҟͳΔೋਓͰ͋Δʹ΋ؔΘΒͣɺ

ཧ࿦͸൒೥ऑఔ౓ͷ౒ྗʹΑͬͯҰ௨Γཧղ͢Δ͜ͱ͕Մೳ

Ͱ͋Δ͜ͱΛɺೋਓ͕ࣗΒͷܦݧΛ΋ͬͯۃΊͯ໌ࣔతͳܗͰཱূͨ͜͠ͱͰ͢ɻ ཧ࿦ͷษڧ͕ࢥ͏Α͏ʹਐ·ͳ͍ݚڀऀ΋ଘࡏ͢ΔΑ͏ͳͷͰɺͦͷΑ͏ͳཱ৔ͷ ݚڀऀʹର͢ΔʮΞυόΠεʯ͕ͳ͍͔ɺࢲ͸ೋਓʹରͯ͠࠶ࡾʹΘͨΓ࣭໰͠ɺ

ٞ࿦ͨ͠ͱ͜Ζɺ།ҰҾ͖ग़͢͜ͱʹ੒ޭͨ͠ʮΞυόΠεʯ͸ɺɹ

ʮ४උͷ࿦จʯ͔Βॱ൪ʹஸೡʹษڧ͢Ε͹ɺ৐Γӽ͑ΒΕͳ͍ো֐͕ग़

ͯ͘Δ͸͕ͣͳ͍

ͱ͍͏झࢫͷൃݴͰͨ͠ɻͨͩɺཧ࿦Λษڧ͢Δ্Ͱͷॏཁͳ஫ҙ఺ͱͯ͠ɺ ɾIUTeichཧ࿦ͷ༷ʑͳݶఆతͳଆ໘ʹ͍ͭͯ͸ෳૉ਺ମɺ͋Δ͍͸pਐମ

্ͷλΠώϛϡʔϥʔཧ࿦΍ɺݹయతͳςʔλؔ਺ͷؔ਺౳ࣜ౳ɺطଘͷ ཧ࿦ͱͷ෦෼తͳྨࣅੑ͸ೝΊΒΕΔ΋ͷͷɺIUTeich ཧ࿦ͷʮຊےʯʹ

ؔͯ͠طଘͷཧ࿦ͱຊ࣭తʹྨࣅͨ͠ύλʔϯͷٞ࿦ͷల։Λظ଴ͯ͠ษ ڧ͠Α͏ͱ͢Δͱ࠳ં͢ΔՄೳੑ͕ߴ͍

͜ͱʹཹҙ͢Δඞཁ͕͋Γ·͢ɻ͜Εʹ͍ͭͯ͸ೋਓͱ΋ಉҙݟͰͨ͠ɻޙɺ࣍ͷ

ೋ఺ʹ͍ͭͯ͸ࢲ͸Կ೥΋લ͔Βසൟʹڧௐ͍ͯ͠·͢ɿ

ɾଟ͘ͷਓ͸ABC༧૝ͷෆ౳ࣜͷ਺஋తͳଆ໘Λओͳؔ৺ͷର৅ͱ͍ͯ͠

ΔΑ͏Ͱ͕͢ɺʮຊ໋ʯͱͯ͠ೝࣝ͞ΕΔ΂͖΋ͷ͸ʮIUTeichཧ࿦ʯͱ

͍͏ཧ࿦ͷํͰ͋Γɺཧ࿦ͱൺֱ͢Δͱɺෆ౳ࣜ͸ཧ࿦͕೗Կʹਂ͍ͱ͜

Ζ·Ͱ۷ΓԼ͍͛ͯΔ΋ͷͰ͋Δ͔Λࣔ͢୯ͳΔʮҰͭͷࢦඪʯʹա͗·

ͤΜɻ

ɾҰ࣌ؒߨԋͲ͜Ζ͔ɺҰिؒఔ౓ͷղઆͰ΋ɺཧ࿦ͷେ·͔ͳ࢓૊ΈΛຊ

֨తʹೲಘͰ͖ΔΑ͏ͳܗͰཧղ͢Δ͜ͱ͸ଟ͘ͷݚڀऀͷ৔߹ɺࠔ೉Ͱ

͋ΓɺͦͷΑ͏ͳ୹ظؒͷ޿ใ׆ಈʹՌͨͯ͠ҙຯ͕͋Δ͔Ͳ͏͔ɺ͜Ε

·ͰͷܦݧΛৼΓฦΔͱɺେ͍ʹٙ໰͕͋ΔΑ͏ʹײ͡·͢ɻҰํɺݸਓ

͕ࠩ͋Δͱ͸͍͑ɺ௨ৗͷ਺࿦زԿʹৄ͍͠ݚڀऀͷ৔߹ɺIUTeichཧ࿦

ΛҰ௨Γཧղ͢Δͷʹʢ্Ͱ΋ࢦఠͨ͠௨Γʣʮ೥୯Ґʯͷ࣌ؒΛඅ΍͢

ඞཁ͸ͳ͘ɺʮ݄୯Ґʯͷ࣌ؒʹ൒೥ఔ౓ͷ࣌ؒ͑͋͞Ε͹ɺे෼ͳ͸ͣ

Ͱ͢ɻ

Sa¨ıdiࢯͱͷަྲྀͷதͰࢲʹͱͬͯಛʹҹ৅తͩͬͨͷ͸ɺࢲ͔ΒͷࢦఠΛ଴ͭ·Ͱ

΋ͳ͘ɺࣗ෼ࣗ਎ͷʮಠཱͳ؍࡯ʯͱͯ͜͠ͷೋ఺ͱಉ༷ͳํ޲ੑͷൃݴΛͯ͠Լ

ͬͨ͜͞ͱͰ͢ɻ ɹ

(9) ࠷ޙʹɺIUTeichཧ࿦ͷݕূ׆ಈʹฒʑͳΒ͵౒ྗͱ೤ҙΛ܏஫͞ΕͨࢁԼࢯͱ

Sa¨ıdiࢯɺฒͼʹ(4)ͷࢀՃऀͨͪʹର͠ɺ͜ͷ৔ΛआΓͯ৺ΑΓް͓͘ྱΛਃ্͠

͛·͢ɻɹ

จݙϦετ

[HASurI] S. Mochizuki, A Survey of the Hodge-Arakelov Theory of Elliptic Curves I, Arithmetic Fundamental Groups and Noncommutative Algebra, Proceedings of Symposia in Pure Mathematics70, American Mathematical Society (2002), pp. 533-569.

[HASurII] S. Mochizuki, A Survey of the Hodge-Arakelov Theory of Elliptic Curves II, Algebraic Geometry 2000, Azumino, Adv. Stud. Pure Math. 36, Math. Soc.

Japan (2002), pp. 81-114.

[SemiAnbd] S. Mochizuki, Semi-graphs of Anabelioids, Publ. Res. Inst. Math. Sci. 42 (2006), pp. 221-322.

[FrdI] S. Mochizuki, The Geometry of Frobenioids I: The General Theory, Kyushu J. Math. 62 (2008), pp. 293-400.

[FrdII] S. Mochizuki, The Geometry of Frobenioids II: Poly-Frobenioids, Kyushu J.

Math. 62 (2008), pp. 401-460.

[EtTh] S. Mochizuki, The ´Etale Theta Function and its Frobenioid-theoretic Mani- festations, Publ. Res. Inst. Math. Sci. 45 (2009), pp. 227-349.

[AbsTopIII] S. Mochizuki, Topics in Absolute Anabelian Geometry III: Global Reconstruc- tion Algorithms, RIMS Preprint 1626 (March 2008).

[GenEll] S. Mochizuki, Arithmetic Elliptic Curves in General Position,Math. J. Okayama Univ. 52 (2010), pp. 1-28.

[IUTchI] S. Mochizuki, Inter-universal Teichm¨uller Theory I: Construction of Hodge Theaters, RIMS Preprint 1756 (August 2012).

[IUTchII] S. Mochizuki,Inter-universal Teichm¨uller Theory II: Hodge-Arakelov-theoretic Evaluation, RIMS Preprint 1757 (August 2012).

[IUTchIII] S. Mochizuki, Inter-universal Teichm¨uller Theory III: Canonical Splittings of the Log-theta-lattice, RIMS Preprint 1758 (August 2012).

[IUTchIV] S. Mochizuki, Inter-universal Teichm¨uller Theory IV: Log-volume Computa- tions and Set-theoretic Foundations, RIMS Preprint 1759 (August 2012).

[Pano] S. Mochizuki, A Panoramic Overview of Inter-universal Teichm¨uller The- ory, RIMS Preprint 1774 (February 2013), to appear in RIMS K¯oky¯uroku Bessatsu.