ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ ژେֶཧղੳॴڀݚɾڭतɹ݄৽Ұ ɹ 2012 8 ݄ʹӉࡍλΠώϛϡʔϥʔཧʢIUTeichʣʹؔ͢Δ࿈ଓจΛൃ ද͠ɺ2013 12 ݄ɺཧͷؔʹূݕ࿈ͨ͠׆ಈʹؔ͢ΔใࠂΛެ։͠·͕ͨ͠ɺ ͦͷޙͷ 1 ͷؒʹ༷ʑͳ৽͍͠ల։͕͋Γ·ͨ͠ͷͰվΊͯ͝ใࠂ͠·͢ɻɹ (1) 2014 ʹߦͳͬͨɺIUTeich ʹؔ͢Δޱ಄ൃද࣍ͷ 2 ݅ʹͳΓ·͢ɿ 2014 02 ݄ 20 ʢ2 ࣌ؒʴ 2 ࣌ؒɺ ژେֶཧղੳॴڀݚͷηϛφʔʣɺ 2014 05 ݄ 24 ʢ2 ࣌ؒʴ 2 ࣌ؒɺ۽ຊେֶʣɻ ྆ํͷߨԋͷϨΫνϟʔϊʔτ͜Ε·Ͱͷ IUTeich ؔ࿈ͷߨԋͷͷΛগ͠मਖ਼ɾ Ճචͨ͠ͷͰ͕͢ɺ͜Ε·ͰͱൺͯଟগΊʹऔΒ͍͍ͤͯͨͩͨߨԋ࣌ؒΛ ͯ͠༻׆ΑΓৄࡉͳղઆௌऺͷ࣭ͷରԠ͕Ͱ͖·ͨ͠ɻϨΫνϟʔϊʔτ ͦͷޙʑमਖ਼͓ͯ͠Γɺ࠷৽൛ʢಉ༷ͳ༰Λղઆͨ͠αʔϕΠʢ[Pano]ʣͱ ʹڞʣࢲͷΤϒαΠτͰެ։͓ͯ͠Γ·͢ɻ2 ݄ͷߨԋओʹཧݚͷେֶӃੜ ͱϙετυΫͷएखɺͦΕ͔Βੲ͔ΒͦͷηϛφʔʹࢀՃ͍ͯ͠Δؔॅࡏݍͷ ͚ऀڀݚͷߨԋͰɺࢀՃऀͷਓ 10ʙ20 ਓఔͰͨ͠ɻҰํɺ5 ݄ͷߨԋ۽ຊ େֶͷՃ౻จڭݩतͷটͰ࣮ͨ͠ݱͷͰɺࢀՃऀभେֶɺभํͷݚ ͕ऀڀଟ͘ɺਓ 40ʙ50 ਓఔͰͨ͠ɻࠓճͷটͷഎʹܠɺ2005 7 ݄ʙ2011 3 ݄ͷؒɺՃ౻ࢯ͕ژେֶֶࣨڭͷ।ڭतΛ͓ͯ͠ΒΕͨࠒɺ 2ʙ3 िؒʹ 1 ճʢʹ 3ʙ4 ࣌ؒఔʣɺ 2 ਓͰߦͳͬͨ IUTeich ͷηϛφʔ͕͋Γ·ͨ͠ɻ࣌ɺIUTeich ·ͩൃల్্ ͷஈ֊ʹ͋ͬͨΘ͚Ͱ͕͢ɺ͝ଟͷ߹ؒΛ๓ͬͯԆʑͱΓ͕ͨΔࢲͷ͓૬खΛ ͯ͠Լͬͨ͞Ճ౻ࢯʹେมँײக͓ͯ͠Γ·͢ɻ (2) ࢁԼ߶ࢯʢژେֶཧղੳॴڀݚཧղੳྲྀަڀݚηϯλʔಛߨࢣʣͱ 2012 10 ݄Ҏ߱ɺIUTeich ʹؔ͢ΔηϛφʔΛߦͳ͓ͬͯΓ·͕͢ɺ2014 ɺ 3 िؒʹ 1 ճʢʹ 4ʙ5 ࣌ؒఔʣɺ IUTeich ʹؔ͢ΔηϛφʔΛߦͳ͍·ͨ͠ɻ͜Ε·Ͱ௨Γ IUTeich ͷ༷ʑͳٕज़త ͳଆ໘ʹ͍ͭͯٞ͠ɺࢁԼࢯ͔Β͍͍ٕͨͩͨज़తͳࢦఠʢʹ 2014 ɺඦ݅ ൃੜͨ͠ 2013 ΑΓେ෯ʹ ͯͬݮ30 ݅ఔʣΛ౿·͑ͯจΛमਖ਼͠ɺमਖ਼൛Λ ࣗͷΤϒαΠτͰެ։͠·ͨ͠ɻࢁԼࢯ 2013 ͔Β IUTeichʢཧʹඞཁ 2 ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ ͳʮ४උͷจʯʣʹؔ͢ΔαʔϕΠͷࣥචΛखֻ͚͓ͯΓɺࣥචͷաఔͰཧͷຊ ମ͕ॻ͔Ε͍ͯΔ࿈ଓจʢ4 รʣΛվΊͯ௨ಡ͠ʢʹ 3 ճʣɺ৽ͨʹ໌࣭ͨ͠ ࢦఠʹ͍ͭͯηϛφʔͰٞ͠·ͨ͠ɻαʔϕΠ 200ʙ300 ทఔʢʹท ͷ্Ͱݪจͷ 1 ׂఔͱ͍͏ڻҟతͳѹॖʂʣͷ͞ʹͳΔࠐݟΈͰɺ࣌ݱ ͰҎ্ॻ͖ऴΘ͍ͬͯΔͱͷ͜ͱͰ͢ɻҰํɺࢁԼࢯभେֶͷాޱ༤ Ұ।ڭतͷটͰ 2014 09 ݄ 16 ʙ19 ͷ 4 ؒʢʹ 1 5 ࣌ؒఔʣɺ भେֶͰ IUTeich ͷ४උͷจʢʹओʹ [AbsTopIII]ʣʹ͍ͭͯߨԋ͠·ͨ͠ɻେ ֶӃੜϙετυΫɺॿڭͷएखΛத৺ʹɺௌऺͷԠ্ʑͩͬͨΑ͏Ͱ͢ɻߨ ԋͰɺIUTeich ʹ͍ͭͯ ͭ·Έ৯͍ͯ͠खͬऔΓૣ͘ཧղ͠Α͏ͱ͢Δͱ 10 ͯͬܦཧղͰ͖ ͳ͍͕ɺ͔ͬ͠Γલ͔Βॱ൪ʹಡΉͱͰཧղͰ͖Δ ͱҙͨͦ͠͏Ͱ͢ɻभେֶͰͷ࿈ଓߨԋͷʮଓ͖ʯ ʢͱ͍͑ɺେͰͷ࿈ଓߨ ԋͷ༰ʹ͍ͭͯ࠷ॳͷؒɺվΊͯղઆ͢Δ༧ఆͰ͋Δʣɺ 2015 03 ݄ 09 ʙ20 ͷʢฏʣ10 ؒʢʹ 1 7 ࣌ؒఔʣɺ ʮRIMS ڞಉڀݚʯʢʹཧݚͷڞಉར༻ࣄۀͷछͷҰͭʣͱͯ͠ཧ͏ͳߦͰݚ ͜ͱʹͳΓ·ͨ͠ɻ͜ͷूձʢʹʮRIMS ڞಉڀݚʯʣͷϓϩάϥϜࢲͷΣϒα ΠτͰެ։͓ͯ͠Γ·͢ɻͳ͓ɺࢁԼࢯͷαʔϕΠΛʢଞͷؔ࿈จͱʹڞʣूձ ͷใࠂूͱ͍͏Ͱܗཧݚͷʮߨڀผʯͱͯ͢͠ߦץΔํͰߟ͓͑ͯΓ·͢ɻ (3) Mohamed Sa¨ıdi ࢯʢΤΫηλʔେֶʢ࿈߹Ԧࠃʣ ɾ।ڭतʣ 2014 06 ݄ 25 ʙ09 ݄ 24 ͷؒɺ ٬һڭतͱͯ͠ཧ͠ࡏʹݚɺࡏؒظதɺཧຊମͷɺʢ࠷ޙͷࢉܭΛআ͍ͨʣ ཧతͳ෦ʢʹ [IUTchI], [IUTchII], [IUTchIII]ʣΛվΊͯ௨ಡ͠ʢʹ 3 ճʣɺ 2013 Նߦͳͬͨηϛφʔͷ༰Λ֬ೝ͠ͳ͕Βɺ৽ͨʹ໌ٕͨ͠ज़తͳ࣭ ࢦఠʢʹશ෦Ͱ 70 ݅ఔʂʣʹ͍ͭͯ ि 1 ճʢʹ 2ʙ3 ࣌ؒఔʷ 9 ճʣ ͷηϛφʔͰࢲͱೋਓͰٞ͠·ͨ͠ɻॳΊͯษ ͨ͠ڧ2013 Նͱൺͯଟ͘ͷٕ ज़తͳෆ۩߹͕ʹط͍ͬͯͨ͜ͱ͋Γɺ2013 ՆΑΓ͔ͳΓಡΈ͘͢ͳͬ ͍ͯͨΑ͏Ͱ͢ɻ2013 Նͷηϛφʔͱಉ༷ʹɺຖिͷηϛφʔͰ͍͍ͨͩͨ Sa¨ıdi ࢯͷʑͷٕज़తͳࢦఠΛ౿·͑ͯจΛमਖ਼͠ɺमਖ਼൛ΛࣗͷΣϒαΠτͰ ެ։͠·ͨ͠ɻηϛφʔͰɺIUTeich ͷී͍ͯͭʹٴɺͲ͏ֻ͕͔ͯ࣌ؒ͠Δ ͷͳͷͰ͘ڧ͔ͭ͠ͳ͍͜ͱΛɺ༔ʑͱۭͨ͠ؾͷԼͰසΓʹઆ͍͓ͯΒ Ε͕ͨ࢟ҹతͰͨ͠ɻ͜Ε͔Β IUTeich ͷษڧΛ࢝ΊΔํͷΞυόΠεʹ͍ͭ ͯվΊͯਘͶͨͱ͜Ζɺ ʮ४උͷจ͔ΒษڧΛ࢝ΊΕɺඞཁͳͷશͯͦ͜ʹ ·ؚΕ͍ͯΔʯ͜ͱΛԿڧௐ͞Ε·ͨ͠ɻ۩ମతʹɺ[IUTchI], [IUTchII] Λ ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ 3 ಡΉʹɺ · · · · [SemiAnbd], §1, §2, §3, §5, §6; [FrdI]; [FrdII], §1, §2, §3; [EtTh] ʢˎʣ; [AbsTopI], §1, §4; [AbsTopII], §3; [AbsTopIII], §1, §2 ʢˎʣ ʢͨͩ͠ɺ ʮʢˎʣʯʮಛʹॏཁʯͰ͋Δ͜ͱΛҙຯ͢Δʣɺ·ͨ [IUTchIII], [IUTchIV] ΛಡΉʹɺߋʹ · [AbsTopIII], §3, §4, §5; · [GenEll] Λษ͢ڧΕΑ͍ɺͱ͍͏Ͱܗʢ͋ΔͷηϛφʔͰʣೋਓͰవΊͯΈ·ͨ͠ɻ (4) ༟ҰࢯʢژେֶཧղੳॴڀݚɾߨࢣʣͱҎલ͔Β༷ʑͳςʔϚͰη ϛφʔΛߦͳ͓ͬͯΓ·͕͢ɺ2014 IUTeich ΛओͨΔςʔϚͱͯ͠ 2 िؒʹ 1 ճʢʹ 3 ࣌ؒఔʣɺ ೋਓͰηϛφʔΛߦͳ͍·ͨ͠ɻࢯͷ߹ɺҎલ͔Βʢʹ 2013 ·ͰʹʣԕΞʔ ϕϧزԿؔ࿈ͷʮ४උͷจʯ ʢʹ [SemiAnbd], [AbsTopI], [AbsTopII], [AbsTopIII]ʣ Λษ͓ͯ͠ڧΓɺࢁͷٕज़తࢦఠΛͯ͠Լ͍ͬͯ͞ΔͷΈͳΒͣɺ[AbsTopIII] ͷ ཧͷԆઢ্ʹ͋Δɺମͷ୯ԕΞʔϕϧزԿʢʹ mono-anabelian geometryʣ ʹؔ͢ΔಠࣗͷڀݚՌಘΒΕ͍ͯ·͢ɻͦͷڀݚՌΛవΊͨෳͷจͷ͏ ͪɺ࠷৽ͷͷΛ 2015 3 ݄ͷूձͷใࠂूʹऩ͢ΔํͰߟ͓͑ͯΓ·͢ɻҰ ํɺࢯͦΕҎ֎ͷ IUTeich ͷʮ४උͷจʯʢʹ [HASurI], [HASurII], [FrdI], [FrdII], [EtTh], [GenEll] ʣΛ 2014 1 ݄ʙ3 ݄·ͰʹಡΈऴ͑ɺ2014 4 ݄ʙ ݄̓ʹֻ͚ͯɺཧͷຊମͷ࿈ଓจʢ4 รʣΛ௨ಡ͠·ͨ͠ɻ࠷ޙͷ͔ॻ͕ࢉܭΕ ͍ͯΔୈ 4 จʢʹ [IUTchIV]ʣҰճ͔͠ಡΈ·ͤΜͰ͕ͨ͠ɺIUTeich ͷཧ తͳ෦͕ॻ͔Ε͍ͯΔୈ 1ʙୈ 3 จʢʹ [IUTchI], [IUTchII], [IUTchIII]ʣɺ ࣗͷཧղΛਂΊΔͨΊʹɺ࠷ऴతʹ 5 ճҎ্௨ಡͨͦ͠͏Ͱ͢ɻࢯͷ߹ɺ 2013 5 ݄ʙ11 ݄ͷؒɺࢁԼࢯ͕։͍ͨ 140 ࣌ؒʹͿٴηϛφʔʹग़੮ͨ͠ܦ ݧΛͰ্ͨܦͷ௨ಡʹͳΓ·͕͢ɺຊମͷཧ͕ॻ͔Ε͍ͯΔจΛ 5 ճҎ্௨ಡ ͯ͠౸ୡͨ͠ཧղΛԾʹʮ100ʯͱ͢ΔͱɺࢁԼࢯͷηϛφʔʹΑͬͯಘΒΕͨ ཧղ͕ͭزҐʹ૬͢Δ͔ਘͶͨͱ͜Ζɺʮ10ʙ15 ఔʯͱͷճΛ͍͖ͨͩ· ͨ͠ɻͦͦʮཧղʯΛશʹԽ͢Δ͜ͱʹແཧ͕͋Γɺ·ͨจΛಡ Έ࢝ΊΔલʹʮॻےʯʹ׳Ε͠Ή্ͰͦͷॻےΛཱʹղઆ͍͍ͯͨͩͨ͠ࢁ ԼࢯͷηϛφʔʹҰఆͷ͋Γ͕ͨΈ͕͋ͬͨͱݴΘΕ·͕ͨ͠ɺͪ͜Βͱͯ͠ ɺཧΛຊ֨తʹཧղ͢Δʹɺ จΛஸೡʹษ͢ڧΔ͜ͱ͕ԿʹඞཁෆՄܽͰ͋Δ͔ɺ վΊͯೝࣝͤ͞͞Ε·ͨ͠ɻ2014 ɺ2 िؒʹ 1 ճࢯͱߦͳͬͨηϛφʔͰ IUTeich ͷଟ༷ͳٕज़తͳଆ໘ʹ͍ͭͯٞ͠·͕ͨ͠ɺͦͷޙɺࢯ͔Β͍ͨͩ ͍༷ͨʑͳٕज़తͳ࣭ࢦఠʢʹશ෦Ͱ 40 ݅ఔʣΛࢀߟʹจΛमਖ਼͠ɺमਖ਼ 4 ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ ൛ΛࣗͷΣϒαΠτͰެ։͠·ͨ͠ɻࢯ͕ཧͷຊମ͕ॻ͔Ε͍ͯΔจΛ ษ࢝͠ڧΊͨஈ֊ͰɺࢁԼࢯͱ Sa¨ıdi ࢯʹΑΔͳ͔ʹط͕ূݕΓਐΜͰ͍ͨͨΊɺ ࡉ͔͍ٕज़తͳෆ۩߹͕͔ͳΓগͳ͘ͳ͍ͬͯͨͦ͏Ͱ͢ɻҰํɺࢯͷ߹ɺԕ ΞʔϕϧزԿͷͰ๛ͳ࣮͕͋ΓɺͦͷԕΞʔϕϧزԿͷਂ͍ཧղΛ༻׆ ͯ͠ཧશମΛ၆ᛌ͢ΔΑ͏ͳͰܗཧͷཧߏΛ͍͍݁ͨͩͨͯ͠ݕՌɺཧ ͷ͋Δ෦ʢʹ۩ମతʹɺମؔ࿈ͷ Kummer ཧʣͷఆࣜԽͷํʹ͓͍ͯ ෆ۩߹͕͋Δ͜ͱ͕໌͠·ͨ͠ɻ͜Εʹ͍ͭͯηϛφʔͰపఈతʹٞ͠ɺͦ ͷෆ۩߹Λղফͨ͠ఆࣜԽͱɺࢯͱͷٞͷओͳ༰Λͨ͠هʮϦϚʔΫʯ͕ॻ ͔Εͨจͷमਖ਼൛Λʢ͍ͭͷΑ͏ʹʣࢲͷΤϒαΠτͰެ։͠·ͨ͠ɻࢯ ͷʑͷࢦఠΛ८Δॲཧ͕Ұஈམͨ͠ळࠒͷ͋ΔͷηϛφʔͰɺIUTeich Λษڧ ͢ΔࢼΈ͕ߤۤ͠࿑͍ͯ͠ΔํͷΞυόΠε͕ͳ͍͔ɺෳճʹΘͨΓਘͶ· ͕ͨ͠ɺࢯ͔Β ࣗͷ߹ɺֶੜͷࠒ͔Β݄ͷ༷ʑͳจΛಡΜͰ͍Δ͕ɺจΛॱ൪ ʹɺஸೡʹษ͢ڧΕཧղ͢Δ͜ͱʹ͍ͭͯʢಛච͢Δఔͷʣۤ࿑Λ͠ ͨ͜ͱͳ͘ɺ࣮ࡍɺࠓճͷ IUTeich ͷ࿈ଓจͷ߹ʢಛච͢Δఔͷʣ ۤ࿑ͳ͔ͬͨ ͱͷʢఆ֎ʹେͳʣճΛ͍͖ͨͩ·ͨ͠ɻ (5) Chung Pang Mok ࢯʢύσϡʔେֶʢΞϝϦΧ߹ऺࠃʣɾ।ڭतʣɺ2014 10 ݄ʙ11 ݄ͷؒɺถࠃͷෳͷେֶ ͍͓ͯʹॴڀݚIUTeich Λհ͢Δߨԋ ΛߦͳͬͨΑ͏Ͱ͢ɻࢲ͜Ε·Ͱ Mok ࢯͱަྲྀͨ͜͠ͱ͕ͳ͘ɺ10 ݄ࠒɺࢯ ͔ΒͷใࠂʹΑͬͯ͜ΕΒͷ׆ಈʹ͍ͭͯΓ·ͨ͠ɻҰํɺ2015 3 ݄ͷूڀݚ ձͷ࣌ ʹظMok ࢯͱަྲྀ͢Δػձ͕८ͬͯ͘Δͱظ͓ͯ͠Γ·͢ɻ (6) ্ͷ (2), (3), (4) Ͱ 3 ໊ͷزԿͷʹऀڀݚΑΔ׆ূݕಈʹ͍ͭͯใࠂ͠· ʮূݕମ੍ʯͷத֩ ͨ͠ɻ͜ͷ 3 ໊ͷऀڀݚ IUTeich ͷʢগͳ͘ͱͰ࣌ݱͷʣ Λ͍ͯ͠Δͱߟ͓͑ͯΓ·͕͢ɺ3 ໊ʹ༷ʑͳڞ௨ͱ૬ҧ͕͋Γ·͢ɻ· ͣɺྸΛͱ͢·͖͍ͯݟɺSa¨ıdi ࢯ 40 ࡀɺࢁԼࢯ 30 ࡀޙɺࢯ 30 ࡀલͱͳ͍ͬͯ·͢ɻྫ͑ɺࢯͷ߹ɺͪΐ͏Ͳ 10 લͷ 2004 य़ͷ ࣌Ͱ·ͩεΩʔϜͷඪ४తͳڭՊॻͰ͋ΔʮHartshorneʯͷॳาతͳ෦Λ ษ͍ͨͯ͠ڧΘ͚Ͱ͔͢ΒɺͦͷΑ͏ͳஈ֊͔Βग़ൃͯ͠ 10 Ҏʹ IUTeich Λʹີݫཧղ͢Δ͜ͱ͕ՄೳͰ͋Δͱ͍͏ɺڵຯਂ͍ʮࣄྫʯʹͳ͍ͬͯ·͢ɻ ʢ ͪΖΜ͜ͷ 10 ͷؒʹɺࢯ IUTeich ͷษڧҎ֎ʹɺ20 ຊఔͷཱͳڀݚ จΛࣥචͨ͠Γɺֶੜͷࢦಋɺूதߨٛɺࠪಡɺॆ࣮ͨ͠ͳڀݚɾڭҭ׆ಈʹै ࣄ͍ͯ͠ΔΘ͚Ͱ͕͢ʂʣ3 ໊ͱͦΕͳΓͷ͕࣮͋ڀݚΔͱʹڞɺֶࡶࢽͷࠪ ಡऀͱͯ͠ͷ๛ͳ࣮ͱݧܦʢʹ 10 ݅Ҏ্ʣ͕͋Γ·͢ɻҰํɺڀݚʹؔ͠ ͍ͯ͏ͱɺSa¨ıdi ࢯͱࢯԕΞʔϕϧزԿͷ͋ͰऀڀݚΓɺԕΞʔϕϧزԿؔ࿈ͷ ๛ͳ͕͋ۀΔͷʹର͠ɺࢁԼࢯͷڀݚԕΞʔϕϧزԿͱجຊతʹؔͷ ͳ͍ɺp ਐϗοδཧ p ਐଟॏθʔλͷΑ͏ͳςʔϚ͕த৺Ͱ͢ɻ͜ͷڀݚ ͷҧ͍Λө͢Δ͔ͷΑ͏ͳܗͷݱʹͳΓ·͕͢ɺSa¨ıdi ࢯͱࢯʢ(3), (4) ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ 5 Ͱͨ͠ٴݴ௨ΓʣԕΞʔϕϧزԿͷԆઢ্ʹ͋Δୈ 1ʙୈ 3 จʢʹ [IUTchI], [IUTchII], [IUTchIII]ʣͰల։͞Ε͍ͯΔཧ͕ओͳؔ৺ͷରͱͳ͍ͬͯͯɺୈ 4 จʢʹ [IUTchIV]ʣͷ۩ମతͳࢉܭ ABC ༧ͷෆࣜɺHodge-Arakelov ཧͱؔ࿈͢Δղੳతͳଆ໘ʹର͢Δؔ৺͕ൺֱతബ͍ͷʹର͠ɺࢁԼࢯୈ 1ʙୈ 3 จͷΈͳΒͣɺୈ 4 จʹରͯ͠૬Ԡͷؔ৺Λʑ͍ࣔͯ͠·͢ɻ͜ ͷΑ͏ʹɺ3 ໊ʹͦΕͧΕͷಛ৭͕͋Γ·͕͢ɺ2013 12 ݄ͷใࠂ্ͷ (2), (3), (4) Ͱղઆͨ͠׆ূݕಈʹ͓͍ͯ 3 ໊ͱۃΊͯॏཁ͔ͭوॏͳߩݙΛ͍ͯ͠ ͯɺ͜Ε·Ͱ͍͍͍ͨͩͯΔʑͷࢦఠΛৼΓฦΔͱվΊͯ௧͢ײΔͱ͜ΖͰ͢ ͕ɺ3 ໊ͷ͏ͪɺͲͷҰਓΛ֎ͯ͠ɺͦͷҰਓͷߩݙܾͯ͠Γͷೋਓͷߩݙ ʹΑͬͯସͰ͖ΔͷͰ͋Γ·ͤΜɻҰํɺ2014 ͷՆࠒ·Ͱͷ׆ূݕಈͰ 3 ໊ͱΜʹަྲྀͯ͠ڞ௨ʹͱͨ͜͡ײͷҰͭɺ2013 ͱҧͬͯʢஶऀͷࢲҎ֎ ͷʣ ʮଞਓʯͱͯ͠ॳΊͯʢ·ͨͦΕʹ͍ۙͰܗʣIUTeich Λຊ֨తʹཧղͨ͠ͱ ͍͏ɺ৽ఱΛΓ։͘ࡍͷ৽͞ਗ਼ʑ͕͍ͩ͠͞ͿബΕ͖͍ͯͯͯɺೡΖ IUTeich ͷ࿈ଓจΛʹࡾ࠶ʹطΘͨΓʢʹ Sa¨ıdi ࢯ 3 ճɺࢁԼࢯ 3 ճҎ্ɺࢯ 5 ճҎ্ʣಡΈ͠ɺ͔͍ͭͯͯ͠ূݕɺ࠷ૣ͜ΕҎ্ɺ Ͳ͜ΛͲ͏ͨ͠ূݕΓʮಥͬࠐΈʯΛೖΕͨΓͨ͠ΒΑ͍͔͔Βͳ͍ɺ زΒ୳ͯ͠৽ͨͳΔূݕର͕ݟͨΒͳ͍ ͱ͍͏ʮωλਚ͖ײʯʹΑΔେ͖ͳʮۭؾͷมԽʯͰ͋Γ·͢ɻߋʹ͏Ұͭɺແ ࢹͰ͖ͳ͍ཁૉͱͯ͠ɺ3 ໊ͱʢͨΓલͰ͕͢ʣIUTeich ͷূݕҎ֎ʹ༷ʑ ͳࣄΛ๊͍͑ͯΔதͰɺ͜ΕҎ্ূݕର͕ݟͨΒͳ͍Α͏ͳঢ়گԼͰ͑ ͯ࡞ۀͷʮۭసʯΛ֮ۀ࡞ূݕͰ·ͯ͠ޛΛܧଓ͢Δ࣌ؒతͳ༨༟͕ͳ͍ͱ͍͏ଆ ໘Λߟྀ͢Δͱɺͪ͜Βͱͯ͜͠ΕҎ্࡞ۀͷܧଓΛ͓͍͢ئΔ͕͍͋߹ےΓ· ͤΜɻ࣮ࡍɺࢲࣗɺ͜Ε·Ͱ 20 ʹΘͨΓɺஶऀɺࠪಡऀɺฤूҕһͦΕ͔Β ฤूҕһͷͦΕͧΕͷཱͰແͷʢߘจͷࠪಡͷʣࣄྫʹؔΘ͖͓ͬͯͯ ΓɺͦͷݧܦΛͨ͠ʹجஅʹͳΓ·͕͢ɺ͜Ε·Ͱͷ 3 ໊ʹΑΔ׆ূݕಈͦͷ ༰ɺపఈͿΓɺ໖ີͿΓ͔Β͑ݴɺ௨ৗͷֶࡶࢽͷࠪಡͷਫ४Λʹطང͔ʹ ্ճ͓ͬͯΓɺʮத֩తͳ 3 ໊ʯҎ֎ͷʹऀڀݚΑΔࢦఠΛೖΕͯɺʢ௨ৗͷ จͷࠪಡͰൃੜ͢ΔΑ͏ͳʣ͙ʹΔΑ͏ͳද໘తͳෆඋɾෆ۩߹ଟൃ͞ݟ Εɺमਖ਼͞Ε͓ͯΓ·͕͢ɺ ཧͷຊےຊ࣭తͳਖ਼൱ʹؔΘΔΑ͏ͳҰ݅֬ೝ͞Ε͓ͯΓ ·ͤΜɻ ࢁԼࢯͱࢯͱͷؒͰަΘ͞ΕͨձͰɺจதͷཧͷهड़ʹ͓͚Δෆ۩߹ ࠓޙൃ͞ݟΕΔՄೳੑ͋Δͱͯ͠ɺཧ͕ຊ࣭తʹؒҧ͍ͬͯΔՄೳੑͳ ͍ͱ͍͏ڞ௨ೝࣝΛ͍࣋ͬͯΔ͜ͱΛ֬ೝͨ͠ͱͷใࠂΛड͚͍ͯ·͢ɻ·ͨཧ ࣗମʹɺݹయతͳΨεੵͷࢉܭςʔλؔͷؔࣜͷূ໌Λ࿈ͤ͞Β ʮ୯ʹຊ ΕΔΑ͏ͳɺʮਘৗͳΒ͟Δඪ४ੑʢʹ canonicalityʣʯ͕͋Γɺͭ·Γɺ ࣭తͳؒҧ͍ͳ͍ʯͱ͍͏ҙຯʹ͓͍ͯʮਖ਼͍͠ཧʯͰ͋ΔͷΈͳΒͣɺ ABC ༧ʹຊ࣭తʹҟͳΔख๏ʹΑΔʮผূ໌ʯ͕Ռͨͯ͠ଘࡏ͠ಘΔ 6 ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ ͔ɺٙΛ๊͔͟ΔΛಘͳ͍ͱ͍͏ҙຯʹ͓͍ͯʮਖ਼͍͠ཧʯͰ͋Δ ͱ͍͏ײΛɺࢲࣗԿ๊͔ͤΒΕͨ͜ͱ͕͋Γɺ·ͨʢࢲͱશʹಠཱ ͳͰܗʣෳͷ͔ऀڀݚΒฉ͔͞Εͨ͜ͱ͕͋Γ·͢ɻ ʢͪΖΜɺޡղ͕ͳ͍Α͏ ʹॻ͍͓͖ͯ·͢ͱɺֶͳີݫతͳҙຯʹ͓͍ͯʮผূ໌ଘࡏ͠ͳ͍ʯͱ͍͏ ໋Λূ໌Ͱ͖ΔΘ͚Ͱ͋Γ·ͤΜʂʣ͜ͷΑ͏ͳঢ়گΛ౿·͑ͯͰ࣌ݱͷ͜ ͪΒͷೝࣝΛ૯ׅ͢Δͱɺ IUTeich ͷূݕɺ࣮࣭తͳֶతͳଆ໘ʹ͓͍ͯࣄ্࣮͍ͯྃ͠Δ ͕ɺཧͷॏཁੑख๏ͷ৽حੑʹྀͯ͠ɺ೦ͷͨΊʮཧ·ͩূݕ தͰ͋Δʯͱ͍͏൘Λ߱Ζ͢લʹ͏গ࣌ؒ͠Λஔ͍ͯΑ͍ ͱߟ͓͑ͯΓ·͢ɻͨͩɺ৻ॏΛͯ͠ظରԠ͢Δ͜ͱʹҰఆͷҙຯ͕͋Δͱͯ͠ ʮূݕதʯͱ͍͏൘Λ߱Ζ͞ͳ͍ͱ͍͏࢟Λ ɺྫ͑͜Ε͔Β 20ʙ30 ͷؒɺ ҡ࣋͢ΔͷԿͳͷ͔ͱߟ͓͑ͯΓɺ༷ʑͳࢉఆͷํ͋Δ͔͠Ε·ͤ Μ͕ɺཧͷ࠷ॳͷޱ಄ൃදʢʹ 2010 10 ݄ͷߨԋʣ࿈ଓจͷެ։ʢʹ 2012 8 ݄ʣΑΓʮ10 Ҏʯͱ͍͏͜ͱͰɺ ʮ2010 ͷޙลΓ·ͰΛ్ͱ͢Δʯ ͜ͱଥͳઢ͔ͱߟ͓͑ͯΓ·͢ɻ (7) ্ͷ (6) ͷ༰Λ౿·͑ͯߟ͑Δͱɺ ࣍ͷεςοϓԿ͔ʁ ͱ͍͏͕ٙવු্͠·͢ɻྫ͑ɺͲͳ͔ͨஶ໊ͳ͕ऀڀݚཧͷਖ਼൱ʹ͍ͭ ܾͯఆతͳൃදΛߦͳ͏ɺͱ͍͏Α͏ͳల։ΛҰ෦ͷֶऀظ͍ͯ͠ΔΑ͏Ͱ ͕͢ɺ͜ͷΑ͏ͳల։͕͍ͭ·Ͱͯͬܦ࣮͍ͳ͠ݱՄೳੑ͕ඇৗʹߴ͍ͱߟ͑ͯ ͓Γ·͢ɻͦͷཧ༝࣍ͷ௨ΓͰ͢ɿҰఆҎ্ͷۀڀݚͷ͋Δऀڀݚͷ߹ɺ จΛಡΉͱ͖ɺ ֶੜॳ৺ऀͷΑ͏ʹʮҰ͔Βֶश͢ΔʯΑ͏ͳ࢟Ͱ࣌ؒΛֻ͚ͯૅج ͔Βॱ൪ʹษ͍ͨͬͱ͍ͯ͘͠ڧΑ͏ͳಡΈํΛྗۃආ͚ɺೡΖ͜Ε·Ͱ ͖͑ͯͨઐࣝਂ͍ཧղΛద༻Ͱ͖ΔΑ͏ʹɺࣗʹͱͬͯʹطʮফ ԽࡁΈʯɺ ʮཧղࡁΈʯͳ༷ʑͳςʔϚͷ͏ͪɺͲΕʹ֘͢Δ๏ͷจ ͳͷ͔ɺจͷओͨΔ༻ޠఆཧΛૉૣ͘ʮࡧݕʯ͢Δ͜ͱʹΑͬͯจ ΛޮΑ͘ʮফԽʯ͠Α͏ͱ͢ΔͷͰ͢ɻ ผͷํ͍ݴΛ͢Εɺ͜ΕࢁԼࢯ͕ҙͨ͠ʮͭ·Έ৯͍ʯʢ্ͷ (2) Λࢀরʣ ͱ͍͏ΞϓϩʔνʹͨΓ·͢ɻҰํɺIUTeich ͷ߹ɺ ʮઈରԕΞʔϕϧزԿʯ ʮΤλʔϧɾςʔλؔͷ߶ੑੑ࣭ʯɺʮHodge-Arakelov ཧʯͱ͍ͬͨςʔϚʹͭ ͍͍ͯਂʹطཧղͱͦΕͳΓͷۀڀݚΛ༗͢ΔͳऀڀݚΒɺͦͷΑ͏ͳʮͭ·Έ ৯͍ʯ͚ͩͰ IUTeich Λ͔ͳΓຊ֨తʹཧղ͢Δ͜ͱ͕Մೳͳͷ͔͠Ε·ͤΜ͕ɺ ͔ෆ͔ผͱͯ͠ɺ͜ΕΒͷςʔϚʹਫ਼௨͍ͯ͠ΔऀڀݚʢࢲࣗΛআ͚ʣ ͜ͷੈʹଘࡏ͠ͳ͍ͷ͕࣮Ͱ͢ɻ͛ڍ͍ͯڧΔͱ͢Εɺ࠷͍ۙʮྲّྀʯͷԕ ΞʔϕϧزԿͷͰڀݚʮҰఆҎ্ʯͷۀڀݚͷ͋Δऀڀݚɺʢ্ͷ (3), (4) ͷʣ ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ 7 Sa¨ıdi ࢯͱࢯɺͦΕ͔Βʢ2013 5 ݄ʙ11 ݄ͷࢁԼࢯͷηϛφʔʹग़੮ͨ͠ʣۄ ٍ҆உࢯʢژେֶཧղੳॴڀݚɾڭतʣͱ͍͏͜ͱʹͳΓ·͢ɻ ʢͨͩ͠ɺۄ ࢯͷ߹ɺଞͷࣄʹΑΓଟΛۃΊ͍ͯΔͨΊɺIUTeich ͷจΛຊ֨తʹษ ͢ڧΔ͜ͱ࣮ݱతͰͳ͍ͱࢥΘΕ·͢ɻʣͭ·ΓɺٞΛཁ͢Δͱɺ ʹطIUTeich ͷ׆ূݕಈʹؔΘ͍ͬͯΔ໊ͷऀڀݚΛআ͚ɺੈքͷશ ͯͷزԿͷऀڀݚʢʹ࿈ଓจ͕ެ։͞Εͨ࣌ʢʹ 2012 8 ݄ʣͰ ͷࢁԼࢯؚΊͯʂʣ IUTeich ͷपลʹ͋Δֶʹؔͯ͠ʮશ͘ͷૉ ਓʯͰ͋Γɺ͜Ε·Ͱͷۀڀݚͷ্ʹΓཱ͍ͬͯΔʮਂ͍ཧղʯΛ׆ ༻ͯ͠ IUTeich ͷਖ਼൱ʹؔ͢Δܾఆతͳʢʹʮֶతʹҙຯͷ͋Δʯʣ ఆΛԼ͢ࢿ͕֨ຊ࣭తʹ͋Γ·ͤΜɻ ͢Δͱɺ ʮ࣍ͷεςοϓԿ͔ʁʯͱ͍͏ֻ͍͚ʹΓ·͕͢ɺ͜ͷΑ͏ͳঢ়Ͱگ ͢ͱɺࢁԼࢯͷΑ͏ʹ ݩʑૉਓͰʮҰ͔Βஸೡʹษ͢ڧΔʯ͜ͱʹΑͬͯཧʹؔ͢Δਂ͍ ཧղʹ౸ୡ͢ΔऀڀݚΛɺʢ߹ʹΑͬͯ૬͍݄Λֻ͚ͯʣগͣ͠ ͭҭ͠૿͍͘͘͠ɺͭ·ΓཧͷීٴΛଅਐ͢ΔͨΊͷྗΛɺظ ʹΘͨΓܧଓ͍ͯ͘͠ ͱ͍ͬͨΑ͏ͳํ͔͠ࢥ͍ු͔ͼ·ͤΜɻҰํɺ ʮҰ͔Βஸೡʹษ͢ڧΔʯ͜ͱʹ ରͯ͠ɺಛʹւ֎ͷऀڀݚΛத৺ʹɺ૬ڧͳ൱ఆతͳݟղڋઈԠ͕ൃੜ͠ ͍ͯΔΑ͏Ͱ͢ɻ্ͷ (2), (3), (4), (6) Ͱղઆͨ͠௨Γɺʮத֩తͳ 3 ໊ʯͷ߹ɺ IUTeich ͷษۃ͕ڧΊͯԁʹਐలͨ͠Θ͚Ͱ͕͢ɺ ҰମͲͷΑ͏ͳݪҼʹΑͬͯʮத֩తͳ 3 ໊ʯͱ͜Ε΄ͲରরతͳԠ ͕ൃੜ͍ͯ͠Δͷ͔ɺͪ͜Βͱͯ͠શ͘ͷಾͰ͋ΓɺͰ࣌ݱղ໌ʹ ࢸ͍ͬͯͳ͍ͱݴΘ͟ΔΛಘ·ͤΜɻ ͨͩ͠ɺ࣍ͷ௨Γɺʮීٴͷোʯͱͳ͍ͬͯΔͷͷʮਖ਼ମʯͳ͍ͦ͠ͷຊ࣭ తͳཧߏΛ८ͬͯɺ͔ͭزͷʢඞͣ͠ʹ͍ޓແؔͰͳ͍ʂʣʮԾઆʯ ͋Γ·͢ɿɹ (H1) IUTeich Λߏ͢Δจͷ߹ܭทʮ४උͷจʯೖΕΔͱઍท ʢʹצఆͷํʹΑͬͯ 1500ʙ2500 ทʣʹ্Δɻท͕ଟ͗ͯ͢ษ͢ڧΔ ࣌ؒྗؾͳ͍ɻ (H2) IUTeich Ͱଟ༻͞ΕΔԕΞʔϕϧزԿܥͷʮ෮ݩ๏ʯͷཧߏɺٞ ͷల։ͷํͦͷഎ͋ʹޙΔʮҙࣝʯΛશ͘ཧղͰ͖ͳ͍ͨΊɺ ؤுͬͯษ͠ڧΑ͏ͱͯٞ͠ʹ͍͍͚ͯͳ͍ɻԕΞʔϕϧزԿʹؔ ͢ΔదͳڭՊॻͷʮڭҭΠϯϑϥʯະͩʹଘࡏ͠ͳ͍ɻɹ (H3) ʹ͓͚Δશͯͷຊ࣭తͳݱϥϯάϥϯζϓϩάϥϜʹݟΒΕΔΑ ͏ͳදݱతͳΞϓϩʔνʹؼண͞ΕΔͱ৴͍ͯ͡Δ͕ɺIUTeich ͷجຊ తͳߟ͑ํͦͷΑ͏ͳදݱతͳΞϓϩʔνʹଇ͍ͬͯΔͷͰͳ͍ɻ 8 ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ (H4) Wiles ͷ 1995 ͷ༗໊ͳʢ༗ཧମ্ͷପԁۂઢʹؔ͢Δʣࣄͷ߹ɺ ༗ཧମҎ֎ͷಛघͳੑ࣭Λ࣋ͬͨମͷ༷ʑͳ֦ுҰൠԽ͕ʹޙ ͳͬͯଞͷʹऀڀݚΑͬͯ͛͠ΒΕ͕ͨɺIUTeich ͷ߹ɺಉ༷ͳ֦ ுҰൠԽʹΑΔ͖Ͱ͕ڀݚΔࠐݟΈ͕ͳ͍ɻʢҼΈʹɺΑ͘ΒΕ͍ͯ ΔΑ͏ʹɺWiles ͷࣄਖ਼ʹ (H3) ͷʮදݱతͳΞϓϩʔνʯͷʮ ද֨ʯͱͯͬݴΑ͍ɻʣ (H5) ࣗࣗͷʹڀݚཱͭʢʹڀݚจͷʮ૿࢈ʯʹ͕ܨΔʣࠐݟΈͷͳ ͍ཧΛษ͢ڧΔՋ͕ͳ͍ɻಛʹ͖ظͷ৬Ͱ࠾༻͞Ε͍ͯΔ 20 ࡀ ʙ30 ࡀͷएखͷऀڀݚͷ߹ɺ͜Ε࣮ͳݒҊࣄ߲Ͱ͋Δɻ ͜ΕΒͷ߲ʹ͍ͭͯɺ·ͣɺ(H1) ͱ (H5)ɺ(H1) ͱ (H2)ɺ(H3) ͱ (H4)ɺͦΕ͔ Β (H4) ͱ (H5) ͷؔ࿈ੑͦΕͧΕͷ߲ͷ༰ΑΓ໌Β͔Ͱ͋Δ͜ͱΛࢦఠͯ͠ ͓͖·͢ɻͦΕͧΕͷ߲ʹؔ͢Δͪ͜Βͷײ࣍ͷ௨ΓʹͳΓ·͢ɿ (T1) ༰ஶऀͷਓɺ༷ʑͳҧ͍͕͋ΔͨΊ୯७ͳൺֱͰ͖·ͤΜ͕ɺ ྫ͑ Weil ༧ͷূ໌ʹ༻͍ΒΕͨ 1960 ͷ༗໊ͳʢεΩʔϜͷج ૅΛங͍ͨʣʮEGAʯͱʮSGAʯͷ߹ܭทʢҰܻଟ͍ʂʣҰສऑҐͷ ทʹ্Γ·͢ɻ (T2) ͔֬ʹڭՊॻͷΑ͏ͳʮڭҭΠϯϑϥʯະͩʹඋ͞Ε͍ͯͳ͍Α͏ Ͱ͢ɻҰํɺ[Qp GC] ͷΑ͏ʹͯ͘ʢʹ 8 ทʂʣॳతʢʹॴہମͷ ʹؔ࿈ͨ͠ݹయతͳཧʹਫ਼௨͍ͯ͠Δಡऀ͔Β͢Εʣ͔ͭೖతͳ จ͋Γ·͢ͷͰɺ͔ͦ͜ΒԕΞʔϕϧزԿͷษڧΛ࢝ΊΔͷҰͭͷ ΞϓϩʔνʹͳΓ·͢ɻͨͩɺࢯʢ্ͷ (4) ͷ࠷ޙลΓͱɺͦΕ͔Β (6) ͷ಄ͷղઆΛࢀরʣΛ࢝ΊɺʹΘͨΓԿ໊ͷֶੜͷڭҭʹؔΘͬ ͨΓɺ·ͨษ͠ڧΑ͏ͱͯۤ͠࿑͍ͯ͠Δͱ͍͏Կ໊ͷऀڀݚͷΛฉ ͍ͨΓ͍ͯ͠Δͱɺ࣍ͷΑ͏ͳҹΛड͚Δ͜ͱ͕গͳ͋͘Γ·ͤΜɿ͜ ͷछͷͷ༗ޮͳରԠʹ࠷ඞཁͳͷɺ ʢڭՊॻͷษʹڧΑΔʣ ৽͍ࣝ͠ͷಋೖͱ͍͏ΑΓɺೡΖʢۤ࿑͍ͯ͠Δͱ͍͏ʣ͕ऀڀݚҎ લ͔ΒʹऔΓೖΕɺʹΘͨΓݻఆͨ͠··ۭؾͷΑ͏ʹͨΓલʹ ৗ༻͍ͯ͠Δ༷ʑͳ ࢥߟճ࿏ΛҰ୴ղআ͠ɺ ಄ΛݴΘʮ·ͬ͞Βʯͳঢ়ଶʹ্ͨ͠Ͱɺֶੜॳ৺ऀͷΑ͏ʹ ࢝ݪతͳཧࢥߟͷΈΛཔΓʹཱͪʹૅجฦͬͯ ࣄΛߟ͑Δ࢟Λపఈ͢Δ͜ͱͰͳ͍Ͱ͠ΐ͏͔ɻ (T3) ϥϯάϥϯζϓϩάϥϜʹද͞ΕΔΑ͏ͳʮදݱతͳΞϓϩʔνʯ ͔֬ʹݱͷେ͖ͳڀݚͷྲྀΕͷҰͭͰ͕͢ɺʹ͓͚Δશͯͷ ຊ࣭తͳݱʮͦͷࡿԼʹೖΔʯɺ͋Δ͍ʮͦͷಛผͳ߹ʹͨΔʯ ͱ͍ͬͨΑ͏ͳߟ͑ํ༷ʑͳॏཁͳతࣄͷ࣮ଶͱ߹͠ͳ͍ͷ Ͱ͋Δͱཧղ͓ͯ͠Γ·͢ɻ ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ 9 (T4) IUTeich ͷҰൠԽͷରͷީิͱͳΓಘΔֶతର͕ݟͨΒͳ͍ຊ࣭ తͳཧ༝ͷҰͭɺIUTeich ͕ʢ༗ཧମͷΑ͏ͳಛघͳମͰͳ͘ʣ ҙͷମʹରͯ͠Γཱͭཧʹͳ͍ͬͯΔ͜ͱʹ͋Γ·͕͢ɺಉ͘͡ҙ ͷମʹରཱͯ͢͠Δ Faltings ͷ༗໊ͳ 1983 ͷࣄͷख๏ɺະͩʹ ଞͷઃఆʹ֦ுɾҰൠԽ͞Ε͍ͯͳ͍ͱೝ͓ࣝͯ͠Γ·͢ɻҰํɺFaltings ͷࣄʹྨࣅݱݟΒΕͳ͍͕ɺ֦ுɾҰൠԽʹ͙ͦΘͳ͍ IUTeich ͷ ͏Ұͭͷॏཁͳଆ໘ͱͯ͠ɺۂతۂઢͷԕΞʔϕϧزԿͱີʹؔ͠ ͍ͯΔପԁۂઢͷςʔλؔͷཧʢʹ [EtTh] ͷཧʣ͕͛ڍΒΕ·͢ɻ (T5) ͔֬ʹɺIUTeich Λਅ໘ʹษ͢ڧΕڀݚจͷʮ૿࢈ʯʹ͕ܨΔ͜ ͱΛࣄલʹอো͢Δ͜ͱͰ͖·ͤΜ͕ɺ͠ʮࣗͷੜʹ׆ཱͭ ͷͰͳ͍ݶΓɺؔ৺͕࣋ͯͳ͍ʯͱ͍͏ཧ۶ʹΑͬͯ IUTeich ͕ଟ͘ͷ زԿͷʹऀڀݚʮسආʯ͞Ε͍ͯΔͱ͢Εɺ IUTeich ͷزԿશମͷதͰͷʮཱͪҐஔʯ ७ਮֶͷਓؒࣾձશମͷதͰͷʮཱͪҐஔʯ ͷׄͷʮ૬ࣅܗͷϞσϧʯͱ͍͏͜ͱʹͳΓɺ͔͠ೋऀʢʹೋछྨͷ ʮཱͪҐஔʯʣͷྨࣅੑΛߟྀ͢ΔͱɺऀޙΛ͢ڀݚΔ্ʹ͓͍ͯɺલऀͷ ਼༗ҙٛͳࣔࠦΛ༩͑ΔՄೳੑΛൿΊ͍ͯΔͱ͍͏ํݟͰ͖ΔͷͰ ͳ͍Ͱ͠ΐ͏͔ɻ ࠷ʹޙɺIUTeich ͷؔʹڀݚΘ͔ͬͯΒेʹΘͨΓଟछଟ༷ͳߠఆతҙݟ൱ ఆతҙ͓͖ͯͯ͠ʹݟΓɺͦͷ͔ݧܦΒੜ·Εͨ͏ҰͭͷײʹͳΓ·͕͢ɺ ཧʹ͍ͭͯʮߠఆର൱ఆʯͱ͍͏ʮରཱ࣠ʯΛೝࣝͤ͞ΒΕΔ͜ͱҰ ͳ͍ͱͤ·͍ݴΜ͕ɺͦͷʮ࣠ʯΑΓೡΖɺड़ΒΕ͍ͯΔҙ͕ݟ ͔ͭີݫదͳֶతཧղͷ্ʹΓཱ͍ͬͯΔͷ͔Ͳ͏͔ ͱ͍͏ʮ࣠ʯͦ͜ɺʮຊ໋ʯͰͳ͍͔ ͱͤ͞͡ײΒΕΔ໘ʹ͠͠ૺ۰͠·͢ɻͨͩ͠ɺͰ࣌ݱ IUTeich ʹ͍ͭ ͯʮ͔ͭີݫదͳֶతཧղͷ্ʹΓཱ͍ͬͯΔʯ൱ఆతͳҙݟΛड़ΒΕ ͨ໘هԱʹ͋Γ·ͤΜɻߠఆɾ൱ఆΛΘͣɺIUTeich ʹ͍͔ͭͯͭີݫద ͳֶతཧղͷ্ʹΓཱ͍ͬͯΔҙݟΛ༗͢Δʹऀڀݚର͢Δఏʹͱ͜͏͍ͱݴ ͳΓ·͕͢ɺɹ ͦͷΑ͏ͳҙݟɺʢࢲΛؚΉʣୈࡾऀͰ͖ͰূݕΔΑ͏ʹɺഎ͋ʹܠ Δֶతͳٞࠜڌͱʹڞωοτ্Ͱʢ͘͠࠷ͰஶऀͰ͋Δ ࢲʹରͯ͠ʣެ։͠ɺIUTeich ʹؔ͢Δɹ ͷཧ ΛਤΔྗΛ͖࣌͢ʹظೖͬͨͷͰͳ͍͔ɺ ͱࢲ͓ͯ͡ײ͘ڧΓ·͢ɻ 10 ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ (8) ্ͷ (6), (7) Ͱղઆͨ͠ঢ়گΛҰͰݴ૯ׅ͢Δͱɺ IUTeich Λ८Δ׆ಈͷॏ৺ʮূݕʯ͔Βʮීٴʯ ͱҠߦͭͭ͋͠Δ࣌͋ʹظΔ͜ͱ͑ݴΔΑ͏ʹࢥ͍·͢ɻࠓޙɺ ʢੈلҎ্ʹٴ Ϳ๛ͳ࣮Λ࣋ͭʣཧݚͷڞಉར༻ࣄۀΛ͢༻׆ΔΑ͏ͳͰܗɺཧݚΛڌ ʹͯ͠ࠃ֎ʹ͚ͯ IUTeich ʹؔ͢Δใൃ৴ɾී׆ٴಈͷऔΓΈΛߋʹڧ Խ͍͖͍ͯͨ͠ͱߟ͓͑ͯΓ·͢ɻւ֎Ͱʢৄ͍͠ঢ়͍ͯͭʹگѲ͓ͯ͠Γ ·ͤΜ͕ʣIUTeich ʹؔ͢Δηϛφʔूڀݚձ͕اը͞ΕͯԿΒ͔ͷҙຯʹ͓ ͍ࣦͯഊʹऴΘΔɺͱ͍͏Α͏ͳΛ͓ͯ͠ʹࣖ͘ͳͱزΓ·͢ɻҰํɺ2015 3 ݄ʹ༧ఆ͍ͯ͠ΔཧͰݚͷूڀݚձͷܭը·Ͱ૨͗ண͚Δ͜ͱ͕Ͱ͖ͨഎʹܠ ɺΓཧʹݚੵ͞Ε͍ͯΔ༷ʑͳܗଶͷࣾձతɾจԽతΠϯϑϥʹΑΔॆ ࣮ͨ͠αϙʔτମ੍͕͋Δ͜ͱΛɺࠓճͷใࠂΛవΊΔʹͨΓվΊͯ௧͓ͯ͠ײ Γ·͢ɻ2015 3 ݄ͷूڀݚձͲͪΒ͔ͱ͍͑ɺࠃͷେֶӃੜएखͷڀݚ ऀΛओͳରͱͯ͠ఆ͍ͯ͠ΔͷͰ͕͢ɺྫ͑ɺཧݚͷࠃࡍަྲྀࣄͰۀɺ ຖւ֎͔Β 300ʙ400 ໊ఔͷظͷདྷ๚ऀɺ ͦΕ͔Β 10ʙ20 ໊ఔͷظʢʹ 1 έ݄Ҏ্ʣͷདྷ๚ऀ ͕ཧݚΛ๚͢Δɺւ֎ͷͱऀڀݚͷަྲྀ͕ΜʹߦͳΘΕ͓ͯΓ·͢ɻதʹ ͜͜ͷ Sa¨ıdi ࢯͷΑ͏ʹɺ٬һڭतͱͯ͠ 3 έ݄Ҏ্ࡏ͢Δ͕ऀڀݚຖ 10 ໊ఔ͓Γ·͢ɻͨͩ͠ɺಛʹࠃࡍަྲྀʹ͍ͭͯԿΒ͔ͷͰܗͷʮ੍ڧʯΛ͘ڧ ओு͢Δਓؒ૬ଘࡏ͢ΔΑ͏Ͱ͕͢ɺࢲ༷ʑͳ͔ݧܦΒɺࠃ֎ͷަྲྀࣄ ۀͷ্ཱͪ͛ʹࡍ͠ɺ ۃڀతͳਅ࣮Λ࢟ͳڏݠͰۃݟΊɺ໌Β͔ʹ͢Δ͜ͱΛ໋ͱ͢ΔҰछ ͷʮऀڀݚʯͷΑ͏ͳࢤͰɺࣄۀͷࢀՃऀͷຊԻͱ͖߹͍ɺ ͦͷຊؾ ΛۃݟΊɺ͔ͬ͠Γ֬ೝͰ͖ͨ߹ʹͷΈࣄۀΛ࣮ߦʹҠ͢ɹ ͱ͍͏࢟Λେʹ͢Δ͜ͱΛੲ͔Βઆ͍͓ͯΓ·͢ɻͦͷΑ͏ͳ࢟ʹ߆Δͷɺ ͦͷΑ͏ʹͯ͠ࢀՃऀͷʮຊؾʯΛ͢༻׆Δ͜ͱΛओମͱ͢Δަྲྀࣄʹۀ ͦ͜ɺ ʢͲΜͳʹաࠅͳฬଧͪΛͬͯͯ͠ʮ੍ڧʯͰ౸ఈΘͳ͍ʂʣ ʹظΘͨΓ࣋ଓ͢Δؾ׆ྗ׆ɺʮ૬ޮՌʯɺਅʹ݈શͳల։ ͕ੜ·ΕΔ ͱ֬৴͍ͯ͠Δ͔ΒͰ͢ɻ࣮ࡍɺྫ͑ɺ · ࢁԼࢯͱͷ IUTeich Λ८Δަྲྀͷ͖͔͚ͬͱͳͬͨͷɺຊਓ͔Βͷ 2012 9 ݄ࠒͷ࿈བྷʹΑΔɺIUTeich Λษ͏͍ͱ͍ͨ͠ڧਃ͠ग़ɺఏҊͰ͋Γɺ ͦͷޙͷαʔϕΠͷࣥචΛؚΊ༷ͨʑͳͰܗͷ׆ূݕಈશͯશʹຊਓ ʹΑΔఏҊͰ͋Γɺࢲ͔ΒͷʮൃҊʯʮґཔʯҰ͋Γ·ͤΜɻ · Sa¨ıdi ࢯͷ߹ɺ2013 7 ݄Ҏ߱ͷ IUTeich Λ८Δަྲྀɺ2013 य़ࠒ ʹʢʹΘͨΓ Sa¨ıdi ࢯͱڞಉڀݚΛߦͳ͍ͬͯΔۄࢯܦ༝Ͱʣ ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ 11 ఔલ͔Β Sa¨ıdi ࢯ͕ʢࢲͱશʹؔͷͳ͍ࣗ͝ͰܗͷҙࢥʹΑΓʂʣ [FrdI] ɺIUTeich ͷษڧΛඪʹɺʮ४උͷจʯͷษʹڧணखͨ͜͠ͱ Λͬͨ͜ͱ͕͖͔͚ͬͰͨ͠ɻ · ࢯͷ߹ɺҎલ͔ΒೋਓͰߦͳ͍ͬͯΔηϛφʔͰ IUTeich ΛऔΓ্ ͛Δʹࢸͬͨͷɺࢲ͕ࢯͱʹΘͨΓࢦಋڭһڞಉͯ͠ͱऀڀݚ ଟछଟ༷ͳԕΞʔϕϧزԿؔ࿈ͷΛࡐʹΜʹަྲྀ͖ͯͨ͜͠ͱ͕ എ͋ʹܠΓ·͕͢ɺͦͷͷަྲྀɺࢯֶ͕෦ੜͷࠒʹʢࢲͱશ ʹؔͷͳ͍ࣗ͝ͰܗͷҙࢥʹΑΓʂʣࢲͷจʢ[pGC]ʣͷ͋Δ෦ ΛಡΜͰɺ͋Δఔཧղ͠ɺp ਐηΫγϣϯ༧ɺp ਐԕΞʔϕϧزԿ Λษ͢ڧΔͨΊʹࢲΛʢम࢜՝ఔͷʣࢦಋڭһʹࢤͯ͠Լͬͨ͜͞ͱ͕ ͖͔͚ͬͰͨ͠ɻ ͳ͓ɺ͜ͷ 3 ໊ͷ߹ɺࢲ͕༷ʑͳจΛࣥචͨ͠Γɺͦͷؔ࿈ͷڀݚΛͨ͠Γ͢ Δ͜ͱʹΑ๊ͬͯ͘ʹࢸͬͨײͰɺจʹ໌ࣔతʹ͔ͨͬͳ͠ࡌهͷͰɺ ࢲ͔ΒͷࢦఠٴݴΛͭ·Ͱͳ͘ɺࣗࣗͷʮಠཱͳ؍ʯͱͯ͠ಉ༷ͳ ༰ͷײΛड़ΒΕͨ͜ͱҰճೋճͰͳ͘ɺͪ͜ΒͰ͖֮͑Εͳ͍΄Ͳ ͷճ͋Γɺͦͷʹେมײಈ͓ͯ͠Γ·͢ɻ͜ͷΑ͏ͳޮՌຊਓͷԢͳҙཉ ͷ্ʹΓཱ͍ͬͯΔ׆ಈͰͳ͍ͱ࣮͢ݱΔͷͰ͋Γ·ͤΜɻ (9) ʮத֩తͳ 3 ໊ʯͷࢁԼࢯɺSa¨ıdi ࢯɺࢯΛ࢝Ίɺ͝ଟͳதɺوॏͳ͓࣌ؒ Λʢ߹ʹΑͬͯେྔʹʣׂ͍ͯࠓճͷใࠂͰղઆ༷ͨ͠ʑͳ׆ಈʹଟେͳߩݙ Λͯ͠Լͬͨؔ͞ऀͷօ༷ͷ֨ผͳΔ͝ҙͱ͝ྱ͓͘ਂʹྗڠΛਃ্͛͠·͢ɻ จݙϦετ [Qp GC] S. Mochizuki, A Version of the Grothendieck Conjecture for p-adic Local Fields, The International Journal of Math. 8 (1997), pp. 499-506. [pGC] S. Mochizuki, The Local Pro-p Anabelian Geometry of Curves, Invent. Math. 138 (1999), pp. 319-423. [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 Mathematics 70, 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. 12 ӉࡍλΠώϛϡʔϥʔཧͷূݕɿਐঢ়گͷใࠂʢ2014 12 ݄ࡏݱʣ [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 Manifestations, Publ. Res. Inst. Math. Sci. 45 (2009), pp. 227-349. [AbsTopI] S. Mochizuki, Topics in Absolute Anabelian Geometry I: Generalities, J. Math. Sci. Univ. Tokyo 19 (2012), pp. 139-242. [AbsTopII] S. Mochizuki, Topics in Absolute Anabelian Geometry II: Decomposition Groups and Endomorphisms, J. Math. Sci. Univ. Tokyo 20 (2013), pp. 171269. [AbsTopIII] S. Mochizuki, Topics in Absolute Anabelian Geometry III: Global Reconstruction 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 Computations and Set-theoretic Foundations, RIMS Preprint 1759 (August 2012). [Pano] S. Mochizuki, A Panoramic Overview of Inter-universal Teichm¨ uller Theory, Algebraic number theory and related topics 2012, RIMS K¯oky¯ uroku Bessatsu B51, Res. Inst. Math. Sci. (RIMS), Kyoto (2014), pp. 301-345.
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