Ӊ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣ‫౎ژ‬େֶ਺ཧղੳ‫ॴڀݚ‬ɾ‫ڭ‬तɹ๬݄৽Ұɹ 2012 ೥ 8 ݄຤ʹӉ஦ࡍλΠώϛϡʔϥʔཧ࿦ʢIUTeichʣʹؔ͢Δ࿈ଓ࿦จΛൃ
ද͠ɺ2013 ೥ 12 ݄ɺཧ࿦ͷ‫ؔʹূݕ‬࿈ͨ͠‫׆‬ಈʹؔ͢ΔใࠂΛެ։͠·͕ͨ͠ɺͦͷ‫ޙ‬ͷ 1 ೥ͷؒʹ༷ʑͳ৽͍͠ల։͕͋Γ·ͨ͠ͷͰվΊͯ͝ใࠂ͠·͢ɻɹ

(1) 2014 ೥ʹߦͳͬͨɺIUTeich ʹؔ͢Δ‫ޱ‬಄ൃද͸࣍ͷ 2 ݅ʹͳΓ·͢ɿ2014 ೥ 02 ݄ 20 ೔ʢ2 ࣌ؒʴ 2 ࣌ؒɺ‫౎ژ‬େֶ਺ཧղੳ‫ॴڀݚ‬ͷ਺࿦ηϛφʔʣɺ2014 ೥ 05 ݄ 24 ೔ʢ2 ࣌ؒʴ 2 ࣌ؒɺ‫۽‬ຊେֶʣɻ྆ํͷߨԋͷϨΫνϟʔϊʔτ͸͜Ε·Ͱͷ IUTeich ؔ࿈ͷߨԋͷ΋ͷΛগ͠मਖ਼ɾՃචͨ͠΋ͷͰ͕͢ɺ͜Ε·Ͱͱൺ΂ͯଟগ௕ΊʹऔΒ͍͍ͤͯͨͩͨߨԋ࣌ؒΛ‫ͯ͠༻׆‬ΑΓৄࡉͳղઆ΍ௌऺͷ࣭໰΁ͷରԠ͕Ͱ͖·ͨ͠ɻϨΫνϟʔϊʔτ ͸ͦͷ‫ޙ‬΋౓ʑमਖ਼͓ͯ͠Γɺ࠷৽൛͸ʢಉ༷ͳ಺༰Λղઆͨ͠αʔϕΠʢ[Pano]ʣͱ‫ʹڞ‬ʣࢲͷ΢ΤϒαΠτͰެ։͓ͯ͠Γ·͢ɻ2 ݄ͷߨԋ͸ओʹ਺ཧ‫ݚ‬ͷେֶӃੜͱϙετυΫ౳ͷएखɺͦΕ͔Βੲ͔ΒͦͷηϛφʔʹࢀՃ͍ͯ͠Δؔ੢‫ॅࡏݍ‬ͷ‫͚޲ऀڀݚ‬ͷߨԋͰɺࢀՃऀͷਓ਺͸ 10ʙ20 ਓఔͰͨ͠ɻҰํɺ5 ݄ͷߨԋ͸‫۽‬ຊେֶͷՃ౻จ‫ڭݩ‬तͷট଴Ͱ࣮‫ͨ͠ݱ‬΋ͷͰɺࢀՃऀ͸‫۝‬भେֶ౳ɺ‫۝‬भ஍ํͷ‫ݚ‬‫͕ऀڀ‬ଟ͘ɺਓ਺͸ 40ʙ50 ਓఔͰͨ͠ɻࠓճͷট଴ͷഎ‫ʹܠ‬ɺ2005 ೥ 7 ݄ʙ2011೥ 3 ݄ͷؒɺՃ౻ࢯ͕‫౎ژ‬େֶ਺ֶ‫ࣨڭ‬ͷ।‫ڭ‬तΛ͓ͯ͠ΒΕͨࠒɺ

2ʙ3 िؒʹ 1 ճʢʹ 3ʙ4 ࣌ؒఔʣɺ
2 ਓͰߦͳͬͨ IUTeich ͷηϛφʔ͕͋Γ·ͨ͠ɻ౰࣌ɺIUTeich ͸·ͩൃల్্ͷஈ֊ʹ͋ͬͨΘ͚Ͱ͕͢ɺ͝ଟ๩ͷ߹ؒΛ๓ͬͯԆʑͱ஻Γ͕ͨΔࢲͷ͓૬खΛͯ͠Լͬͨ͞Ճ౻ࢯʹେม‫ँײ‬க͓ͯ͠Γ·͢ɻ(2) ࢁԼ߶ࢯʢ‫౎ژ‬େֶ਺ཧղੳ‫਺ॴڀݚ‬ཧղੳ‫ྲྀަڀݚ‬ηϯλʔಛ೚ߨࢣʣͱ͸2012 ೥ 10 ݄Ҏ߱ɺIUTeich ʹؔ͢ΔηϛφʔΛߦͳ͓ͬͯΓ·͕͢ɺ2014 ೥΋ɺ
3 िؒʹ 1 ճʢʹ 4ʙ5 ࣌ؒఔʣɺ
IUTeich ʹؔ͢ΔηϛφʔΛߦͳ͍·ͨ͠ɻ͜Ε·Ͱ௨Γ IUTeich ͷ༷ʑͳٕज़తͳଆ໘ʹ͍ͭͯٞ࿦͠ɺࢁԼࢯ͔Β͍͍ٕͨͩͨज़తͳࢦఠʢʹ 2014 ೥͸ɺ਺ඦ݅ൃੜͨ͠ 2013 ೥ΑΓେ෯ʹ‫ ͯͬݮ‬30 ݅ఔ౓ʣΛ౿·͑ͯ࿦จΛमਖ਼͠ɺमਖ਼൛Λࣗ෼ͷ΢ΤϒαΠτͰެ։͠·ͨ͠ɻࢁԼࢯ͸ 2013 ೥͔Β IUTeichʢ΍ཧ࿦ʹඞཁ2Ӊ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣͳʮ४උͷ࿦จʯʣʹؔ͢ΔαʔϕΠͷࣥචΛखֻ͚͓ͯΓɺࣥචͷաఔͰཧ࿦ͷຊମ͕ॻ͔Ε͍ͯΔ࿈ଓ࿦จʢ4 รʣΛվΊͯ௨ಡ͠ʢʹ 3 ճ໨ʣɺ৽ͨʹ൑໌࣭ͨ͠໰΍ࢦఠʹ͍ͭͯηϛφʔͰٞ࿦͠·ͨ͠ɻαʔϕΠ͸ 200ʙ300 ทఔ౓ʢʹท਺ͷ্Ͱ͸‫ݪ‬࿦จͷ 1 ׂఔ౓ͱ͍͏‫ڻ‬ҟతͳѹॖ཰ʂʣͷ௕͞ʹͳΔ‫ࠐݟ‬ΈͰɺ‫࣌ݱ‬఺Ͱ͸൒෼Ҏ্ॻ͖ऴΘ͍ͬͯΔͱͷ͜ͱͰ͢ɻҰํɺࢁԼࢯ͸‫۝‬भେֶͷా‫ޱ‬༤Ұ࿠।‫ڭ‬तͷট଴Ͱ

2014 ೥ 09 ݄ 16 ೔ʙ19 ೔ͷ 4 ೔ؒʢʹ 1 ೔ 5 ࣌ؒఔʣɺ
‫۝‬भେֶͰ IUTeich ͷ४උͷ࿦จʢʹओʹ [AbsTopIII]ʣʹ͍ͭͯߨԋ͠·ͨ͠ɻେֶӃੜ΍ϙετυΫɺॿ‫ڭ‬౳ͷएखΛத৺ʹɺௌऺͷ൓Ԡ͸্ʑͩͬͨΑ͏Ͱ͢ɻߨԋͰ͸ɺIUTeich ʹ͍ͭͯͭ·Έ৯͍ͯ͠खͬऔΓૣ͘ཧղ͠Α͏ͱ͢Δͱ 10 ೥‫ͯͬܦ‬΋ཧղͰ͖ͳ͍͕ɺ͔ͬ͠Γલ͔Βॱ൪ʹಡΉͱ൒೥ͰཧղͰ͖Δͱ஫ҙͨͦ͠͏Ͱ͢ɻ‫۝‬भେֶͰͷ࿈ଓߨԋͷʮଓ͖ʯʢͱ͸͍͑ɺ‫۝‬େͰͷ࿈ଓߨԋͷ಺༰ʹ͍ͭͯ͸࠷ॳͷ਺೔ؒɺվΊͯղઆ͢Δ༧ఆͰ͋Δʣ͸ɺ

2015 ೥ 03 ݄ 09 ೔ʙ20 ೔ͷʢฏ೔ʣ10 ೔ؒʢʹ 1 ೔ 7 ࣌ؒఔʣɺʮRIMS ‫ڞ‬ಉ‫ڀݚ‬ʯʢʹ਺ཧ‫ݚ‬ͷ‫ڞ‬ಉར༻ࣄ‫ۀ‬ͷछ໨ͷҰͭʣͱͯ͠਺ཧ‫͏ͳߦͰݚ‬͜ͱʹͳΓ·ͨ͠ɻ͜ͷूձʢʹʮRIMS ‫ڞ‬ಉ‫ڀݚ‬ʯʣͷϓϩάϥϜ͸ࢲͷ΢ΣϒαΠτͰެ։͓ͯ͠Γ·͢ɻͳ͓ɺࢁԼࢯͷαʔϕΠΛʢଞͷؔ࿈࿦จͱ‫ʹڞ‬ʣूձͷใࠂूͱ͍͏‫਺Ͱܗ‬ཧ‫ݚ‬ͷʮߨ‫ڀ‬࿥ผ࡭ʯͱͯ͠‫͢ߦץ‬Δํ޲Ͱߟ͓͑ͯΓ·͢ɻ

(3) Mohamed Saı̈di ࢯʢΤΫηλʔେֶʢ࿈߹Ԧࠃʣ
ɾ।‫ڭ‬तʣ͸2014 ೥ 06 ݄ 25 ೔ʙ09 ݄ 24 ೔ͷؒɺ٬һ‫ڭ‬तͱͯ͠਺ཧ‫͠ࡏ଺ʹݚ‬ɺ଺ࡏ‫ؒظ‬தɺཧ࿦ຊମͷɺʢ࠷‫ޙ‬ͷ‫ࢉܭ‬Λআ͍ͨʣཧ࿦తͳ෦෼ʢʹ [IUTchI], [IUTchII], [IUTchIII]ʣΛվΊͯ௨ಡ͠ʢʹ 3 ճ໨ʣɺ2013 ೥Նߦͳͬͨηϛφʔͷ಺༰Λ֬ೝ͠ͳ͕Βɺ৽ͨʹ൑໌ٕͨ͠ज़తͳ࣭໰΍ࢦఠʢʹશ෦Ͱ 70 ݅ఔʂʣʹ͍ͭͯि 1 ճʢʹ 2ʙ3 ࣌ؒఔ౓ʷ 9 ճʣͷηϛφʔͰࢲͱೋਓͰٞ࿦͠·ͨ͠ɻॳΊͯษ‫ ͨ͠ڧ‬2013 ೥Նͱൺ΂ͯଟ͘ͷٕज़తͳෆ۩߹͕‫ʹط‬௚͍ͬͯͨ͜ͱ΋͋Γɺ2013 ೥ՆΑΓ͸͔ͳΓಡΈ΍͘͢ͳ͍ͬͯͨΑ͏Ͱ͢ɻ2013 ೥Նͷηϛφʔͱಉ༷ʹɺຖिͷηϛφʔͰ͍͍ͨͩͨ Saı̈diࢯͷ਺ʑͷٕज़తͳࢦఠΛ౿·͑ͯ࿦จΛमਖ਼͠ɺमਖ਼൛Λࣗ෼ͷ΢ΣϒαΠτͰެ։͠·ͨ͠ɻηϛφʔͰ͸ɺIUTeich ͷී‫͍ͯͭʹٴ‬ɺͲ͏ͯ͠΋ֻ͕͔࣌ؒΔ΋ͷͳͷͰ೜଱‫͘ڧ‬଴͔ͭ͠ͳ͍͜ͱΛɺ༔ʑͱۭͨ͠‫ؾ‬ͷԼͰසΓʹઆ͍͓ͯΒΕ͕ͨ࢟ҹ৅తͰͨ͠ɻ͜Ε͔Β IUTeich ͷษ‫ڧ‬Λ࢝ΊΔํ΁ͷΞυόΠεʹ͍ͭͯվΊͯਘͶͨͱ͜Ζɺʮ४උͷ࿦จ͔Βษ‫ڧ‬Λ࢝ΊΕ͹ɺඞཁͳ΋ͷ͸શͯͦ͜ʹ‫·ؚ‬Ε͍ͯΔʯ͜ͱΛԿ౓΋‫ڧ‬ௐ͞Ε·ͨ͠ɻ۩ମతʹ͸ɺ[IUTchI], [IUTchII] ΛӉ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣ3ಡΉʹ͸ɺ· [SemiAnbd], §1, §2, §3, §5, §6;· [FrdI]; [FrdII], §1, §2, §3;· [EtTh] ʢˎʣ;· [AbsTopI], §1, §4; [AbsTopII], §3; [AbsTopIII], §1, §2 ʢˎʣʢͨͩ͠ɺʮʢˎʣʯ͸ʮಛʹॏཁʯͰ͋Δ͜ͱΛҙຯ͢Δʣɺ·ͨ [IUTchIII], [IUTchIV]ΛಡΉʹ͸ɺߋʹ· [AbsTopIII], §3, §4, §5;· [GenEll]
Λษ‫͢ڧ‬Ε͹Α͍ɺͱ͍͏‫Ͱܗ‬ʢ͋Δ೔ͷηϛφʔͰʣೋਓͰవΊͯΈ·ͨ͠ɻ(4) ੕༟Ұ࿠ࢯʢ‫౎ژ‬େֶ਺ཧղੳ‫ॴڀݚ‬ɾߨࢣʣͱ͸Ҏલ͔Β༷ʑͳςʔϚͰηϛφʔΛߦͳ͓ͬͯΓ·͕͢ɺ2014 ೥͸ IUTeich ΛओͨΔςʔϚͱͯ͠
2 िؒʹ 1 ճʢʹ 3 ࣌ؒఔ౓ʣɺೋਓͰηϛφʔΛߦͳ͍·ͨ͠ɻ੕ࢯͷ৔߹ɺҎલ͔Βʢʹ 2013 ೥຤·ͰʹʣԕΞʔϕϧ‫ز‬Կؔ࿈ͷʮ४උͷ࿦จʯʢʹ [SemiAnbd], [AbsTopI], [AbsTopII], [AbsTopIII]ʣ
Λษ‫͓ͯ͠ڧ‬Γɺ୔ࢁͷٕज़తࢦఠΛͯ͠Լ͍ͬͯ͞ΔͷΈͳΒͣɺ[AbsTopIII] ͷཧ࿦ͷԆ௕ઢ্ʹ͋Δɺ਺ମͷ୯ԕΞʔϕϧ‫ز‬Կʢʹ mono-anabelian geometryʣʹؔ͢Δಠࣗͷ‫ڀݚ‬੒Ռ΋ಘΒΕ͍ͯ·͢ɻͦͷ‫ڀݚ‬੒ՌΛవΊͨෳ਺ͷ࿦จͷ͏ͪɺ࠷৽ͷ΋ͷΛ 2015 ೥ 3 ݄ͷूձͷใࠂूʹऩ࿥͢Δํ޲Ͱߟ͓͑ͯΓ·͢ɻҰํɺ੕ࢯ͸ͦΕҎ֎ͷ IUTeich ͷʮ४උͷ࿦จʯʢʹ [HASurI], [HASurII], [FrdI],[FrdII], [EtTh], [GenEll] ౳ʣΛ 2014 ೥ 1 ݄ʙ3 ݄·ͰʹಡΈऴ͑ɺ2014 ೥ 4 ݄ʙ݄̓ʹֻ͚ͯɺཧ࿦ͷຊମͷ࿈ଓ࿦จʢ4 รʣΛ௨ಡ͠·ͨ͠ɻ࠷‫ޙ‬ͷ‫͔ॻ͕ࢉܭ‬Ε
͍ͯΔୈ 4 ࿦จʢʹ [IUTchIV]ʣ͸Ұճ͔͠ಡΈ·ͤΜͰ͕ͨ͠ɺIUTeich ͷཧ࿦తͳ෦෼͕ॻ͔Ε͍ͯΔୈ 1ʙୈ 3 ࿦จʢʹ [IUTchI], [IUTchII], [IUTchIII]ʣ͸ɺࣗ෼ͷཧղΛਂΊΔͨΊʹɺ࠷ऴతʹ͸ 5 ճҎ্௨ಡͨͦ͠͏Ͱ͢ɻ੕ࢯͷ৔߹ɺ2013 ೥ 5 ݄ʙ11 ݄ͷؒɺࢁԼࢯ͕։͍ͨ໿ 140 ࣌ؒʹ‫Ϳٴ‬ηϛφʔʹग़੮ͨ͠‫ܦ‬‫ݧ‬Λ‫Ͱ্ͨܦ‬ͷ௨ಡʹͳΓ·͕͢ɺຊମͷཧ࿦͕ॻ͔Ε͍ͯΔ࿦จΛ 5 ճҎ্௨ಡͯ͠౸ୡͨ͠ཧղ౓ΛԾʹʮ100ʯͱ͢ΔͱɺࢁԼࢯͷηϛφʔʹΑͬͯಘΒΕͨཧղ౓͕‫ͭز‬Ґʹ૬౰͢Δ͔ਘͶͨͱ͜Ζɺʮ10ʙ15 ఔ౓ʯͱͷճ౴Λ͍͖ͨͩ·ͨ͠ɻͦ΋ͦ΋ʮཧղ౓ʯΛ‫׬‬શʹ਺஋Խ͢Δ͜ͱʹ͸ແཧ͕͋Γɺ·ͨ࿦จΛಡΈ࢝ΊΔલʹʮ‫ॻے‬ʯʹ‫׳‬Ε਌͠Ή্Ͱ͸ͦͷ‫ॻے‬Λཱ೿ʹղઆ͍͍ͯͨͩͨ͠ࢁԼࢯͷηϛφʔʹ͸Ұఆͷ͋Γ͕ͨΈ͕͋ͬͨͱ΋‫ݴ‬ΘΕ·͕ͨ͠ɺͪ͜Βͱͯ͠͸ɺཧ࿦Λຊ֨తʹཧղ͢Δʹ͸ɺ࿦จΛஸೡʹษ‫͢ڧ‬Δ͜ͱ͕೗ԿʹඞཁෆՄܽͰ͋Δ͔ɺվΊͯೝࣝͤ͞͞Ε·ͨ͠ɻ2014 ೥ɺ2 िؒʹ 1 ճ੕ࢯͱߦͳͬͨηϛφʔͰ͸
IUTeich ͷଟ༷ͳٕज़తͳଆ໘ʹ͍ͭͯٞ࿦͠·͕ͨ͠ɺͦͷ‫ޙ‬ɺ੕ࢯ͔Β͍͍༷ͨͩͨʑͳٕज़తͳ࣭໰΍ࢦఠʢʹશ෦Ͱ 40 ݅ఔ౓ʣΛࢀߟʹ࿦จΛमਖ਼͠ɺमਖ਼4Ӊ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣ൛Λࣗ෼ͷ΢ΣϒαΠτͰެ։͠·ͨ͠ɻ੕ࢯ͕ཧ࿦ͷຊମ͕ॻ͔Ε͍ͯΔ࿦จΛษ‫࢝͠ڧ‬Ίͨஈ֊Ͱ͸ɺࢁԼࢯͱ Saı̈di ࢯʹΑΔ‫ͳ͔ʹط͕ূݕ‬ΓਐΜͰ͍ͨͨΊɺࡉ͔͍ٕज़తͳෆ۩߹͕͔ͳΓগͳ͘ͳ͍ͬͯͨͦ͏Ͱ͢ɻҰํɺ੕ࢯͷ৔߹ɺԕΞʔϕϧ‫ز‬Կͷ෼໺Ͱ͸๛෋ͳ࣮੷͕͋ΓɺͦͷԕΞʔϕϧ‫ز‬Կͷਂ͍ཧղΛ‫༻׆‬ͯ͠ཧ࿦શମΛ၆ᛌ͢ΔΑ͏ͳ‫Ͱܗ‬ཧ࿦ͷ࿦ཧߏ଄Λ఺‫͍͍݁ͨͩͨͯ͠ݕ‬Ռɺཧ࿦ͷ͋Δ෦෼ʢʹ۩ମతʹ͸ɺ਺ମؔ࿈ͷ Kummer ཧ࿦ʣͷఆࣜԽͷ࢓ํʹ͓͍ͯෆ۩߹͕͋Δ͜ͱ͕൑໌͠·ͨ͠ɻ͜Εʹ͍ͭͯ͸ηϛφʔͰపఈతʹٞ࿦͠ɺͦͷෆ۩߹Λղফͨ͠ఆࣜԽͱɺ੕ࢯͱͷٞ࿦ͷओͳ಺༰Λ‫ͨ͠ه‬ʮϦϚʔΫʯ͕ॻ͔Εͨ࿦จͷमਖ਼൛Λʢ͍ͭ΋ͷΑ͏ʹʣࢲͷ΢ΤϒαΠτͰެ։͠·ͨ͠ɻ੕ࢯͷ਺ʑͷࢦఠΛ८Δॲཧ͕Ұஈམͨ͠ळࠒͷ͋Δ೔ͷηϛφʔͰɺIUTeich Λษ‫ڧ‬͢ΔࢼΈ͕೉ߤۤ͠࿑͍ͯ͠Δํ΁ͷΞυόΠε͕ͳ͍͔ɺෳ਺ճʹΘͨΓਘͶ·͕ͨ͠ɺ੕ࢯ͔Β͸ࣗ෼ͷ৔߹ɺֶੜͷࠒ͔Β๬݄ͷ༷ʑͳ࿦จΛಡΜͰ͍Δ͕ɺ࿦จΛॱ൪ʹɺஸೡʹษ‫͢ڧ‬Ε͹ཧղ͢Δ͜ͱʹ͍ͭͯ͸ʢಛච͢Δఔͷʣۤ࿑Λͨ͜͠ͱ͸ͳ͘ɺ࣮ࡍɺࠓճͷ IUTeich ͷ࿈ଓ࿦จͷ৔߹΋ʢಛච͢Δఔͷʣۤ࿑͸ͳ͔ͬͨͱͷʢ૝ఆ֎ʹ‫׮‬େͳʣճ౴Λ͍͖ͨͩ·ͨ͠ɻ

(5) Chung Pang Mok ࢯʢύσϡʔେֶʢΞϝϦΧ߹ऺࠃʣɾ।‫ڭ‬तʣ͸ɺ2014೥ 10 ݄ʙ11 ݄ͷؒɺถࠃͷෳ਺ͷେֶ΍‫ ͍͓ͯʹॴڀݚ‬IUTeich Λ঺հ͢ΔߨԋΛߦͳͬͨΑ͏Ͱ͢ɻࢲ͸͜Ε·Ͱ Mok ࢯͱަྲྀͨ͜͠ͱ͕ͳ͘ɺ10 ݄ࠒɺ੕ࢯ͔ΒͷใࠂʹΑͬͯ͜ΕΒͷ‫׆‬ಈʹ͍ͭͯ஌Γ·ͨ͠ɻҰํɺ2015 ೥ 3 ݄ͷ‫ूڀݚ‬ձͷ࣌‫ ʹظ‬Mok ࢯͱަྲྀ͢Δ‫ػ‬ձ͕८ͬͯ͘Δͱ‫ظ‬଴͓ͯ͠Γ·͢ɻ(6) ্ͷ (2), (3), (4) Ͱ͸ 3 ໊ͷ਺࿦‫ز‬Կͷ‫ʹऀڀݚ‬ΑΔ‫׆ূݕ‬ಈʹ͍ͭͯใࠂ͠·ʮ‫ূݕ‬ମ੍ʯͷத֩ͨ͠ɻ͜ͷ 3 ໊ͷ‫ऀڀݚ‬͸ IUTeich ͷʢগͳ͘ͱ΋‫Ͱ఺࣌ݱ‬ͷʣΛ੒͍ͯ͠Δͱߟ͓͑ͯΓ·͕͢ɺ3 ໊ʹ͸༷ʑͳ‫ڞ‬௨఺ͱ૬ҧ఺͕͋Γ·͢ɻ·ͣɺ೥ྸΛ‫ͱ͢·͖͍ͯݟ‬ɺSaı̈di ࢯ͸ 40 ࡀ୅൒͹ɺࢁԼࢯ͸ 30 ࡀ୅‫ޙ‬൒ɺ੕ࢯ͸
30 ࡀ୅લ൒ͱͳ͍ͬͯ·͢ɻྫ͑͹ɺ੕ࢯͷ৔߹ɺͪΐ͏Ͳ 10 ೥લͷ 2004 ೥य़ͷ࣌఺Ͱ͸·ͩεΩʔϜ࿦ͷඪ४తͳ‫ڭ‬ՊॻͰ͋ΔʮHartshorneʯͷॳาతͳ෦෼Λษ‫͍ͨͯ͠ڧ‬Θ͚Ͱ͔͢ΒɺͦͷΑ͏ͳஈ֊͔Βग़ൃͯ͠΋ 10 ೥Ҏ಺ʹ IUTeichΛ‫ʹີݫ‬ཧղ͢Δ͜ͱ͕ՄೳͰ͋Δͱ͍͏ɺ‫ڵ‬ຯਂ͍ʮࣄྫʯʹͳ͍ͬͯ·͢ɻʢ΋ͪΖΜ͜ͷ 10 ೥ͷؒʹɺ੕ࢯ͸ IUTeich ͷษ‫ڧ‬Ҏ֎ʹ΋ɺ20 ຊఔͷཱ೿ͳ‫ڀݚ‬࿦จΛࣥචͨ͠Γɺֶੜͷࢦಋɺूதߨٛɺࠪಡ౳ɺॆ࣮ͨ͠ͳ‫ڀݚ‬ɾ‫ڭ‬ҭ‫׆‬ಈʹैࣄ͍ͯ͠ΔΘ͚Ͱ͕͢ʂʣ3 ໊ͱ΋ͦΕͳΓͷ‫͕͋੷࣮ڀݚ‬Δͱ‫ʹڞ‬ɺ਺ֶࡶࢽͷࠪಡऀͱͯ͠ͷ๛෋ͳ‫੷࣮ͱݧܦ‬ʢʹ 10 ݅Ҏ্ʣ͕͋Γ·͢ɻҰํɺ‫ڀݚ‬෼໺ʹ͍ؔͯ͠͏ͱɺSaı̈di ࢯͱ੕ࢯ͸ԕΞʔϕϧ‫ز‬Կͷ‫͋Ͱऀڀݚ‬ΓɺԕΞʔϕϧ‫ز‬Կؔ࿈ͷ๛෋ͳ‫͕͋੷ۀ‬Δͷʹର͠ɺࢁԼࢯͷ‫ڀݚ‬͸ԕΞʔϕϧ‫ز‬Կͱ͸‫ج‬ຊతʹ͸ؔ܎ͷͳ͍ɺp ਐϗοδཧ࿦΍ p ਐଟॏθʔλ஋ͷΑ͏ͳςʔϚ͕த৺Ͱ͢ɻ͜ͷ‫ڀݚ‬෼໺ͷҧ͍Λ൓ө͢Δ͔ͷΑ͏ͳ‫ܗ‬ͷ‫ݱ‬৅ʹͳΓ·͕͢ɺSaı̈di ࢯͱ੕ࢯ͸ʢ(3), (4)Ӊ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣ5Ͱ΋‫ͨ͠ٴݴ‬௨ΓʣԕΞʔϕϧ‫ز‬ԿͷԆ௕ઢ্ʹ͋Δୈ 1ʙୈ 3 ࿦จʢʹ [IUTchI],[IUTchII], [IUTchIII]ʣͰల։͞Ε͍ͯΔཧ࿦͕ओͳؔ৺ͷର৅ͱͳ͍ͬͯͯɺୈ 4࿦จʢʹ [IUTchIV]ʣͷ۩ମతͳ‫ࢉܭ‬΍ ABC ༧૝ͷෆ౳ࣜ౳ɺHodge-Arakelovཧ࿦ͱؔ࿈͢Δղੳ਺࿦తͳଆ໘ʹର͢Δؔ৺͕ൺֱతബ͍ͷʹର͠ɺࢁԼࢯ͸ୈ
1ʙୈ 3 ࿦จͷΈͳΒͣɺୈ 4 ࿦จʹରͯ͠΋૬Ԡͷؔ৺Λ౓ʑ͍ࣔͯ͠·͢ɻ͜ͷΑ͏ʹɺ3 ໊ʹ͸ͦΕͧΕͷಛ৭͕͋Γ·͕͢ɺ2013 ೥ 12 ݄ͷใࠂ΍্ͷ (2),(3), (4) Ͱղઆͨ͠‫׆ূݕ‬ಈʹ͓͍ͯ 3 ໊ͱ΋‫ۃ‬Ίͯॏཁ͔ͭ‫و‬ॏͳߩ‫ݙ‬Λ͍ͯͯ͠ɺ͜Ε·Ͱ͍͍͍ͨͩͯΔ਺ʑͷࢦఠ౳ΛৼΓฦΔͱվΊͯ௧‫͢ײ‬Δͱ͜ΖͰ͢
͕ɺ3 ໊ͷ͏ͪɺͲͷҰਓΛ֎ͯ͠΋ɺͦͷҰਓͷߩ‫ݙ‬͸ܾͯ͠࢒Γͷೋਓͷߩ‫ݙ‬ʹΑͬͯ୅ସͰ͖Δ΋ͷͰ͸͋Γ·ͤΜɻҰํɺ2014 ೥ͷՆࠒ·Ͱͷ‫׆ূݕ‬ಈͰ 3໊ͱ΋੝Μʹަྲྀͯ͠‫ڞ‬௨ʹ‫ͱͨ͜͡ײ‬ͷҰͭ͸ɺ2013 ೥ͱҧͬͯʢஶऀͷࢲҎ֎ͷʣʮଞਓʯͱͯ͠ॳΊͯʢ·ͨ͸ͦΕʹ͍ۙ‫Ͱܗ‬ʣIUTeich Λຊ֨తʹཧղͨ͠ͱ͍͏ɺ৽ఱ஍Λ੾Γ։͘ࡍͷ৽઱͞΍ਗ਼ʑ͕͍ͩ͠͞ͿബΕ͖͍ͯͯͯɺೡΖIUTeich ͷ࿈ଓ࿦จΛ‫ʹࡾ࠶ʹط‬ΘͨΓʢʹ Saı̈di ࢯ͸ 3 ճɺࢁԼࢯ͸ 3ճҎ্ɺ੕ࢯ͸ 5 ճҎ্ʣಡΈ௚͠ɺ͔ͭ‫͍ͯͯ͠ূݕ‬ɺ࠷ૣ͜ΕҎ্ɺͲ͜ΛͲ͏‫ͨ͠ূݕ‬ΓʮಥͬࠐΈʯΛೖΕͨΓͨ͠ΒΑ͍͔෼͔Βͳ͍ɺ‫ز‬Β୳ͯ͠΋৽ͨͳΔ‫ূݕ‬ର৅͕‫ݟ‬౰ͨΒͳ͍ͱ͍͏ʮωλਚ͖‫ײ‬ʯʹΑΔେ͖ͳʮۭ‫ؾ‬ͷมԽʯͰ͋Γ·͢ɻߋʹ΋͏ҰͭɺແࢹͰ͖ͳ͍ཁૉͱͯ͠ɺ3 ໊ͱ΋ʢ౰ͨΓલͰ͕͢ʣIUTeich ͷ‫ূݕ‬Ҏ֎ʹ΋༷ʑͳ࢓ࣄΛ๊͍͑ͯΔதͰɺ͜ΕҎ্‫ূݕ‬ର৅͕‫ݟ‬౰ͨΒͳ͍Α͏ͳঢ়‫گ‬ԼͰ΋‫͑׶‬ͯ࡞‫ۀ‬ͷʮۭసʯΛ֮‫ۀ࡞ূݕͰ·ͯ͠ޛ‬Λ‫ܧ‬ଓ͢Δ࣌ؒతͳ༨༟͕ͳ͍ͱ͍͏ଆ໘Λߟྀ͢Δͱɺͪ͜Βͱͯ͠΋͜ΕҎ্࡞‫ۀ‬ͷ‫ܧ‬ଓΛ͓‫͍͢ئ‬Δ‫͕͍͋߹ے‬Γ·ͤΜɻ࣮ࡍɺࢲࣗ਎ɺ͜Ε·Ͱ 20 ਺೥ʹΘͨΓɺஶऀɺࠪಡऀɺฤूҕһͦΕ͔Βฤूҕһ௕ͷͦΕͧΕͷཱ৔Ͱແ਺ͷʢ౤ߘ࿦จͷࠪಡͷʣࣄྫʹؔΘ͖͓ͬͯͯΓɺͦͷ‫ݧܦ‬Λ‫ͨ͠ʹج‬൑அʹͳΓ·͕͢ɺ͜Ε·Ͱͷ 3 ໊ʹΑΔ‫׆ূݕ‬ಈ͸ͦͷ಺༰ɺపఈͿΓɺ໖ີͿΓ͔Β‫͑ݴ‬͹ɺ௨ৗͷ਺ֶࡶࢽͷࠪಡͷਫ४Λ‫ʹط‬ང͔ʹ্ճ͓ͬͯΓɺʮத֩తͳ 3 ໊ʯҎ֎ͷ‫ʹऀڀݚ‬ΑΔࢦఠ౳ΛೖΕͯ΋ɺʢ௨ৗͷ࿦จͷࠪಡͰൃੜ͢ΔΑ͏ͳʣ௚͙ʹ௚ΔΑ͏ͳද໘తͳෆඋɾෆ۩߹͸ଟ਺ൃ‫͞ݟ‬Εɺमਖ਼͞Ε͓ͯΓ·͕͢ɺཧ࿦ͷຊ‫ے‬΍ຊ࣭తͳਖ਼൱ʹؔΘΔΑ͏ͳ໰୊఺͸Ұ݅΋֬ೝ͞Ε͓ͯΓ·ͤΜɻࢁԼࢯͱ੕ࢯͱͷؒͰަΘ͞Εͨձ࿩Ͱ΋ɺ࿦จதͷཧ࿦ͷ‫ه‬ड़ʹ͓͚Δෆ۩߹͸ࠓ‫ޙ‬΋ൃ‫͞ݟ‬ΕΔՄೳੑ͸͋Δͱͯ͠΋ɺཧ࿦͕ຊ࣭తʹؒҧ͍ͬͯΔՄೳੑ͸ͳ͍ͱ͍͏‫ڞ‬௨ೝࣝΛ͍࣋ͬͯΔ͜ͱΛ֬ೝͨ͠ͱͷใࠂΛड͚͍ͯ·͢ɻ·ͨཧ࿦ࣗମʹ͸ɺ‫ݹ‬యతͳΨ΢εੵ෼ͷ‫ࢉܭ‬΍ςʔλؔ਺ͷؔ਺౳ࣜͷূ໌Λ࿈૝ͤ͞Βʮ୯ʹຊΕΔΑ͏ͳɺʮਘৗͳΒ͟Δඪ४ੑʢʹ canonicalityʣʯ͕͋Γɺͭ·Γɺ࣭తͳؒҧ͍͸ͳ͍ʯͱ͍͏ҙຯʹ͓͍ͯʮਖ਼͍͠ཧ࿦ʯͰ͋ΔͷΈͳΒͣɺABC ༧૝ʹ͸ຊ࣭తʹҟͳΔख๏ʹΑΔʮผূ໌ʯ͕Ռͨͯ͠ଘࡏ͠ಘΔ

6Ӊ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣ͔ɺٙ໰Λ๊͔͟ΔΛಘͳ͍ͱ͍͏ҙຯʹ͓͍ͯ΋ʮਖ਼͍͠ཧ࿦ʯͰ͋Δͱ͍͏‫ײ‬૝Λɺࢲࣗ਎΋Կ౓΋๊͔ͤΒΕͨ͜ͱ͕͋Γɺ·ͨʢࢲͱ͸‫׬‬શʹಠཱͳ‫Ͱܗ‬ʣෳ਺ͷ‫͔ऀڀݚ‬Βฉ͔͞Εͨ͜ͱ͕͋Γ·͢ɻʢ΋ͪΖΜɺ‫ޡ‬ղ͕ͳ͍Α͏ʹॻ͍͓͖ͯ·͢ͱɺ‫ֶ਺ͳີݫ‬తͳҙຯʹ͓͍ͯʮผূ໌͸ଘࡏ͠ͳ͍ʯͱ͍͏໋୊Λূ໌Ͱ͖ΔΘ͚Ͱ͸͋Γ·ͤΜʂʣ͜ͷΑ͏ͳঢ়‫گ‬Λ౿·͑ͯ‫Ͱ఺࣌ݱ‬ͷͪ͜ΒͷೝࣝΛ૯‫ׅ͢‬Δͱɺ

IUTeich ͷ‫ূݕ‬͸ɺ࣮࣭తͳ਺ֶతͳଆ໘ʹ͓͍ͯࣄ্࣮‫͍ͯྃ͠׬‬Δ͕ɺཧ࿦ͷॏཁੑ΍ख๏ͷ৽‫ح‬ੑʹ഑ྀͯ͠ɺ೦ͷͨΊʮཧ࿦͸·ͩ‫ূݕ‬தͰ͋Δʯͱ͍͏‫؃‬൘Λ߱Ζ͢લʹ΋͏গ࣌ؒ͠Λஔ͍ͯ΋Α͍ͱߟ͓͑ͯΓ·͢ɻͨͩɺ৻ॏΛ‫ͯ͠ظ‬ରԠ͢Δ͜ͱʹ͸Ұఆͷҙຯ͕͋Δͱͯ͠ʮ‫ূݕ‬தʯͱ͍͏‫؃‬൘Λ߱Ζ͞ͳ͍ͱ͍͏࢟੎Λ΋ɺྫ͑͹͜Ε͔Β 20ʙ30 ೥ͷؒɺҡ࣋͢Δͷ͸೗Կͳ΋ͷ͔ͱ΋ߟ͓͑ͯΓɺ༷ʑͳࢉఆͷ࢓ํ͸͋Δ͔΋͠Ε·ͤΜ͕ɺཧ࿦ͷ࠷ॳͷ‫ޱ‬಄ൃදʢʹ 2010 ೥ 10 ݄ͷߨԋʣ΍࿈ଓ࿦จͷެ։ʢʹ 2012
೥ 8 ݄ʣΑΓʮ10 ೥Ҏ಺ʯͱ͍͏͜ͱͰɺ
ʮ2010 ೥୅ͷ‫ޙ‬൒ลΓ·ͰΛ໨్ͱ͢Δʯ͜ͱ͸ଥ౰ͳઢ͔ͱߟ͓͑ͯΓ·͢ɻ(7) ্ͷ (6) ͷ಺༰Λ౿·͑ͯߟ͑Δͱɺ࣍ͷεςοϓ͸Կ͔ʁͱ͍͏ٙ໰͕౰વු্͠·͢ɻྫ͑͹ɺͲͳ͔ͨஶ໊ͳ‫͕ऀڀݚ‬ཧ࿦ͷਖ਼൱ʹ͍ܾͭͯఆతͳൃදΛߦͳ͏ɺͱ͍͏Α͏ͳల։ΛҰ෦ͷ਺ֶऀ͸‫ظ‬଴͍ͯ͠ΔΑ͏Ͱ͕͢ɺ͜ͷΑ͏ͳల։͕͍ͭ·Ͱ‫ͯͬܦ‬΋࣮‫͍ͳ͠ݱ‬Մೳੑ͕ඇৗʹߴ͍ͱߟ͓͑ͯΓ·͢ɻͦͷཧ༝͸࣍ͷ௨ΓͰ͢ɿҰఆҎ্ͷ‫੷ۀڀݚ‬ͷ͋Δ‫ऀڀݚ‬ͷ৔߹ɺ࿦จΛಡΉͱ͖ɺֶੜ΍ॳ৺ऀͷΑ͏ʹʮҰ͔Βֶश͢ΔʯΑ͏ͳ࢟੎Ͱ࣌ؒΛֻ͚ͯ‫ૅج‬͔Βॱ൪ʹษ‫͍ͨͬͱ͍ͯ͘͠ڧ‬Α͏ͳಡΈํΛ‫ྗۃ‬ආ͚ɺೡΖ͜Ε·Ͱ஝͖͑ͯͨઐ໳஌ࣝ΍ਂ͍ཧղΛద༻Ͱ͖ΔΑ͏ʹɺࣗ෼ʹͱͬͯ‫ʹط‬ʮফԽࡁΈʯɺʮཧղࡁΈʯͳ༷ʑͳςʔϚͷ͏ͪɺͲΕʹ֘౰͢Δ࿦๏ͷ࿦จͳͷ͔ɺ࿦จͷओͨΔ༻‫ޠ‬΍ఆཧΛૉૣ͘ʮ‫ࡧݕ‬ʯ͢Δ͜ͱʹΑͬͯ࿦จΛޮ཰Α͘ʮফԽʯ͠Α͏ͱ͢ΔͷͰ͢ɻผͷ‫ํ͍ݴ‬Λ͢Ε͹ɺ͜Ε͸ࢁԼࢯ͕஫ҙͨ͠ʮͭ·Έ৯͍ʯʢ্ͷ (2) Λࢀরʣͱ͍͏Ξϓϩʔνʹ౰ͨΓ·͢ɻҰํɺIUTeich ͷ৔߹ɺʮઈରԕΞʔϕϧ‫ز‬Կʯ΍ʮΤλʔϧɾςʔλؔ਺ͷ߶ੑੑ࣭ʯɺʮHodge-Arakelov ཧ࿦ʯͱ͍ͬͨςʔϚʹ͍ͭͯ‫͍ਂʹط‬ཧղͱͦΕͳΓͷ‫੷ۀڀݚ‬Λ༗͢Δ‫ͳऀڀݚ‬ΒɺͦͷΑ͏ͳʮͭ·Έ৯͍ʯ͚ͩͰ IUTeich Λ͔ͳΓຊ֨తʹཧղ͢Δ͜ͱ͕Մೳͳͷ͔΋͠Ε·ͤΜ͕ɺ޾͔ෆ޾͔͸ผͱͯ͠ɺ͜ΕΒͷςʔϚʹਫ਼௨͍ͯ͠Δ‫ऀڀݚ‬͸ʢࢲࣗ਎Λআ͚͹ʣ͜ͷੈʹଘࡏ͠ͳ͍ͷ͕࣮৘Ͱ͢ɻ‫͛ڍ͍ͯڧ‬Δͱ͢Ε͹ɺ࠷΋͍ۙʮྲّྀʯͷԕΞʔϕϧ‫ز‬Կͷ‫Ͱڀݚ‬ʮҰఆҎ্ʯͷ‫੷ۀڀݚ‬ͷ͋Δ‫ऀڀݚ‬͸ɺʢ্ͷ (3), (4) ͷʣӉ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣ7Saı̈di ࢯͱ੕ࢯɺͦΕ͔Βʢ2013 ೥ 5 ݄ʙ11 ݄ͷࢁԼࢯͷηϛφʔʹग़੮ͨ͠ʣ‫ۄ‬઒ٍ҆உࢯʢ‫౎ژ‬େֶ਺ཧղੳ‫ॴڀݚ‬ɾ‫ڭ‬तʣͱ͍͏͜ͱʹͳΓ·͢ɻʢͨͩ͠ɺ‫ۄ‬઒ࢯͷ৔߹ɺଞͷ࢓ࣄʹΑΓଟ๩Λ‫ۃ‬Ί͍ͯΔͨΊɺIUTeich ͷ࿦จΛຊ֨తʹษ‫͢ڧ‬Δ͜ͱ͸౰෼‫࣮ݱ‬తͰ͸ͳ͍ͱࢥΘΕ·͢ɻʣͭ·Γɺٞ࿦Λཁ໿͢Δͱɺ‫ ʹط‬IUTeich ͷ‫׆ূݕ‬ಈʹؔΘ͍ͬͯΔ਺໊ͷ‫ऀڀݚ‬Λআ͚͹ɺੈքͷશͯͷ਺࿦‫ز‬Կͷ‫ऀڀݚ‬ʢʹ࿈ଓ࿦จ͕ެ։͞Εͨ࣌఺ʢʹ 2012 ೥ 8 ݄ʣͰͷࢁԼࢯ΋‫ؚ‬Ίͯʂʣ͸ IUTeich ͷपลʹ͋Δ਺ֶʹؔͯ͠͸ʮશ͘ͷૉਓʯͰ͋Γɺ͜Ε·Ͱͷ‫੷ۀڀݚ‬ͷ্ʹ੒Γཱ͍ͬͯΔʮਂ͍ཧղʯΛ‫׆‬༻ͯ͠ IUTeich ͷਖ਼൱ʹؔ͢Δܾఆతͳʢʹʮ਺ֶతʹҙຯͷ͋Δʯʣ൑ఆΛԼ͢ࢿ͕֨ຊ࣭తʹ͋Γ·ͤΜɻ͢Δͱɺʮ࣍ͷεςοϓ͸Կ͔ʁʯͱ͍͏໰ֻ͍͚ʹ໭Γ·͕͢ɺ͜ͷΑ͏ͳঢ়‫Ͱگ‬͢ͱɺࢁԼࢯͷΑ͏ʹ‫ݩ‬ʑ͸ૉਓͰ΋ʮҰ͔Βஸೡʹษ‫͢ڧ‬Δʯ͜ͱʹΑͬͯཧ࿦ʹؔ͢Δਂ͍ཧղʹ౸ୡ͢Δ‫ऀڀݚ‬Λɺʢ৔߹ʹΑͬͯ૬౰௕͍೥݄Λֻ͚ͯʣগͣͭ͠ҭ੒͠૿΍͍͘͘͠ɺͭ·Γཧ࿦ͷී‫ٴ‬Λଅਐ͢ΔͨΊͷ౒ྗΛɺ௕‫ظ‬ʹΘͨΓ‫ܧ‬ଓ͍ͯ͘͠ͱ͍ͬͨΑ͏ͳํ਑͔͠ࢥ͍ු͔ͼ·ͤΜɻҰํɺʮҰ͔Βஸೡʹษ‫͢ڧ‬Δʯ͜ͱʹରͯ͠ɺಛʹւ֎ͷ‫ऀڀݚ‬Λத৺ʹɺ૬౰‫ڧ‬྽ͳ൱ఆతͳ‫ݟ‬ղ΍‫ڋ‬ઈ൓Ԡ͕ൃੜ͍ͯ͠ΔΑ͏Ͱ͢ɻ্ͷ (2), (3), (4), (6) Ͱղઆͨ͠௨Γɺʮத֩తͳ 3 ໊ʯͷ৔߹ɺ
IUTeich ͷษ‫ۃ͕ڧ‬Ίͯԁ‫ʹ׈‬ਐలͨ͠Θ͚Ͱ͕͢ɺҰମͲͷΑ͏ͳ‫ݪ‬ҼʹΑͬͯʮத֩తͳ 3 ໊ʯͱ͜Ε΄Ͳ΋ରরతͳ൓Ԡ
͕ൃੜ͍ͯ͠Δͷ͔ɺͪ͜Βͱͯ͠͸શ͘ͷಾͰ͋Γɺ‫Ͱ఺࣌ݱ‬͸ղ໌ʹࢸ͍ͬͯͳ͍ͱ‫ݴ‬Θ͟ΔΛಘ·ͤΜɻͨͩ͠ɺ࣍ͷ௨Γɺʮී‫ٴ‬ͷো֐ʯͱͳ͍ͬͯΔ΋ͷͷʮਖ਼ମʯͳ͍͠͸ͦͷຊ࣭తͳ࿦ཧߏ଄Λ८ͬͯɺ‫͔ͭز‬ͷʢඞͣ͠΋‫ʹ͍ޓ‬ແؔ܎Ͱ͸ͳ͍ʂʣʮԾઆʯ͸͋Γ·͢ɿɹ

(H1) IUTeich Λߏ੒͢Δ࿦จͷ߹‫ܭ‬ท਺͸ʮ४උͷ࿦จʯ΋ೖΕΔͱ਺ઍทʢʹ‫צ‬ఆͷ࢓ํʹΑͬͯ 1500ʙ2500 ทʣʹ্Δɻท਺͕ଟ͗ͯ͢ษ‫͢ڧ‬Δ࣌ؒ΋‫ྗؾ‬΋ͳ͍ɻ(H2) IUTeich Ͱଟ༻͞ΕΔԕΞʔϕϧ‫ز‬Կ‫ܥ‬ͷʮ෮‫ݩ‬࿦๏ʯͷ࿦ཧߏ଄ɺٞ࿦ͷల։ͷ࢓ํ΍ͦͷഎ‫͋ʹޙ‬Δʮ໰୊ҙࣝʯ౳Λશ͘ཧղͰ͖ͳ͍ͨΊɺ‫ؤ‬ுͬͯษ‫͠ڧ‬Α͏ͱͯ͠΋ٞ࿦ʹ෇͍͍͚ͯͳ͍ɻԕΞʔϕϧ‫ز‬Կʹؔ͢Δద੾ͳ‫ڭ‬Պॻ౳ͷʮ‫ڭ‬ҭΠϯϑϥʯ΋ະͩʹଘࡏ͠ͳ͍ɻɹ
(H3) ਺࿦ʹ͓͚Δશͯͷຊ࣭తͳ‫ݱ‬৅͸ϥϯάϥϯζϓϩάϥϜʹ‫ݟ‬ΒΕΔΑ͏ͳද‫ݱ‬࿦తͳΞϓϩʔνʹ‫ؼ‬ண͞ΕΔͱ৴͍ͯ͡Δ͕ɺIUTeich ͷ‫ج‬ຊతͳߟ͑ํ͸ͦͷΑ͏ͳද‫ݱ‬࿦తͳΞϓϩʔνʹଇ͍ͬͯΔ΋ͷͰ͸ͳ͍ɻ8Ӊ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣ(H4) Wiles ͷ 1995 ೥ͷ༗໊ͳʢ༗ཧ਺ମ্ͷପԁ‫ۂ‬ઢʹؔ͢Δʣ࢓ࣄͷ৔߹ɺ༗ཧ਺ମҎ֎ͷಛघͳੑ࣭Λ࣋ͬͨ਺ମ౳΁ͷ༷ʑͳ֦ு΍ҰൠԽ͕‫ʹޙ‬ͳͬͯଞͷ‫ʹऀڀݚ‬Αͬͯ੒͠਱͛ΒΕ͕ͨɺIUTeich ͷ৔߹ɺಉ༷ͳ֦ு΍ҰൠԽʹΑΔ‫͖Ͱ͕ڀݚ‬Δ‫ࠐݟ‬Έ͕ͳ͍ɻʢҼΈʹɺΑ͘஌ΒΕ͍ͯΔΑ͏ʹɺWiles ͷ࢓ࣄ͸ਖ਼ʹ (H3) ͷʮද‫ݱ‬࿦తͳΞϓϩʔνʯͷʮ୅ද֨ʯͱ‫ͯͬݴ‬Α͍ɻʣ(H5) ࣗ෼ࣗ਎ͷ‫ʹڀݚ‬໾ཱͭʢʹ‫ڀݚ‬࿦จͷʮ૿࢈ʯʹ‫͕ܨ‬Δʣ‫ࠐݟ‬Έͷͳ͍ཧ࿦Λษ‫͢ڧ‬ΔՋ͕ͳ͍ɻಛʹ೚‫͖෇ظ‬ͷ৬Ͱ࠾༻͞Ε͍ͯΔ 20 ࡀ୅ʙ30 ࡀ୅ͷएखͷ‫ऀڀݚ‬ͷ৔߹ɺ͜Ε͸੾࣮ͳ‫ݒ‬Ҋࣄ߲Ͱ͋Δɻ͜ΕΒͷ߲໨ʹ͍ͭͯɺ·ͣɺ(H1) ͱ (H5)ɺ(H1) ͱ (H2)ɺ(H3) ͱ (H4)ɺͦΕ͔
Β (H4) ͱ (H5) ͷؔ࿈ੑ͸ͦΕͧΕͷ߲໨ͷ಺༰ΑΓ໌Β͔Ͱ͋Δ͜ͱΛࢦఠ͓͖ͯ͠·͢ɻͦΕͧΕͷ߲໨ʹؔ͢Δͪ͜Βͷ‫ײ‬૝͸࣍ͷ௨ΓʹͳΓ·͢ɿ

(T1) ಺༰΍ஶऀͷਓ਺౳ɺ༷ʑͳҧ͍͕͋ΔͨΊ୯७ͳൺֱ͸Ͱ͖·ͤΜ͕ɺྫ͑͹ Weil ༧૝ͷূ໌ʹ༻͍ΒΕͨ 1960 ೥୅ͷ༗໊ͳʢεΩʔϜ࿦ͷ‫ج‬ૅΛங͍ͨʣʮEGAʯͱʮSGAʯͷ߹‫ܭ‬ท਺͸ʢҰܻଟ͍ʂʣҰສऑҐͷท਺ʹ্Γ·͢ɻ
(T2) ͔֬ʹ‫ڭ‬ՊॻͷΑ͏ͳʮ‫ڭ‬ҭΠϯϑϥʯ͸ະͩʹ੔උ͞Ε͍ͯͳ͍Α͏Ͱ͢ɻҰํɺ[Qp GC] ͷΑ͏ʹ୹ͯ͘ʢʹ 8 ทʂʣॳ౳తʢʹ‫ॴہ‬ମͷ੔਺࿦ʹؔ࿈ͨ͠‫ݹ‬యతͳཧ࿦ʹਫ਼௨͍ͯ͠Δಡऀ͔Β͢Ε͹ʣ͔ͭೖ໳తͳ࿦จ΋͋Γ·͢ͷͰɺ͔ͦ͜ΒԕΞʔϕϧ‫ز‬Կͷษ‫ڧ‬Λ࢝ΊΔͷ͸ҰͭͷΞϓϩʔνʹͳΓ·͢ɻͨͩɺ੕ࢯʢ্ͷ (4) ͷ࠷‫ޙ‬ลΓͱɺͦΕ͔Β (6)ͷ๯಄ͷղઆΛࢀরʣΛ࢝Ίɺ௕೥ʹΘͨΓԿ໊΋ͷֶੜͷ‫ڭ‬ҭʹؔΘͬͨΓɺ·ͨษ‫͠ڧ‬Α͏ͱͯۤ͠࿑͍ͯ͠Δͱ͍͏Կ໊΋ͷ‫ऀڀݚ‬ͷ࿩Λฉ͍ͨΓ͍ͯ͠Δͱɺ࣍ͷΑ͏ͳҹ৅Λड͚Δ͜ͱ͕গͳ͋͘Γ·ͤΜɿ͜ͷछͷ໰୊΁ͷ༗ޮͳରԠʹ࠷΋ඞཁͳ΋ͷ͸ɺʢ‫ڭ‬Պॻ౳ͷษ‫ʹڧ‬ΑΔʣ
৽͍͠஌ࣝͷಋೖͱ͍͏ΑΓ΋ɺೡΖʢۤ࿑͍ͯ͠Δͱ͍͏ʣ‫͕ऀڀݚ‬Ҏલ͔Β೴ʹऔΓೖΕɺ௕೥ʹΘͨΓ‫ݻ‬ఆͨ͠··ۭ‫ؾ‬ͷΑ͏ʹ౰ͨΓલʹৗ༻͍ͯ͠Δ༷ʑͳࢥߟճ࿏ΛҰ୴ղআ͠ɺ಄Λ‫ݴ‬Θ͹ʮ·ͬ͞Βʯͳঢ়ଶʹ্ͨ͠Ͱɺֶੜ΍ॳ৺ऀͷΑ͏ʹ‫࢝ݪ‬తͳ࿦ཧࢥߟͷΈΛཔΓʹ‫ཱͪʹૅج‬ฦͬͯ෺ࣄΛߟ͑Δ࢟੎Λపఈ͢Δ͜ͱͰ͸ͳ͍Ͱ͠ΐ͏͔ɻ(T3) ϥϯάϥϯζϓϩάϥϜʹ୅ද͞ΕΔΑ͏ͳʮද‫ݱ‬࿦తͳΞϓϩʔνʯ͸͔֬ʹ‫ݱ‬୅਺࿦ͷେ͖ͳ‫ڀݚ‬ͷྲྀΕͷҰͭͰ͕͢ɺ਺࿦ʹ͓͚Δશͯͷຊ࣭తͳ‫ݱ‬৅͸ʮͦͷࡿԼʹೖΔʯɺ͋Δ͍͸ʮͦͷಛผͳ৔߹ʹ౰ͨΔʯͱ͍ͬͨΑ͏ͳߟ͑ํ͸༷ʑͳॏཁͳ਺࿦తࣄ৅ͷ࣮ଶͱ੔߹͠ͳ͍΋ͷͰ͋Δͱཧղ͓ͯ͠Γ·͢ɻӉ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣ9(T4) IUTeich ͷҰൠԽͷର৅ͷީิͱͳΓಘΔ਺ֶతର৅͕‫ݟ‬౰ͨΒͳ͍ຊ࣭తͳཧ༝ͷҰͭ͸ɺIUTeich ͕ʢ༗ཧ਺ମͷΑ͏ͳಛघͳ਺ମͰ͸ͳ͘ʣ೚ҙͷ਺ମʹରͯ͠੒Γཱͭཧ࿦ʹͳ͍ͬͯΔ͜ͱʹ͋Γ·͕͢ɺಉ͘͡೚ҙͷ਺ମʹରͯ͠੒ཱ͢Δ Faltings ͷ༗໊ͳ 1983 ೥ͷ࢓ࣄͷख๏΋ɺະͩʹଞͷઃఆʹ֦ுɾҰൠԽ͞Ε͍ͯͳ͍ͱೝ͓ࣝͯ͠Γ·͢ɻҰํɺFaltingsͷ࢓ࣄʹྨࣅ‫ݱ‬৅͸‫ݟ‬ΒΕͳ͍͕ɺ֦ுɾҰൠԽʹ͙ͦΘͳ͍ IUTeich ͷ΋͏Ұͭͷॏཁͳଆ໘ͱͯ͠ɺ૒‫ۂ‬త‫ۂ‬ઢͷԕΞʔϕϧ‫ز‬Կͱີ઀ʹؔ܎͍ͯ͠Δପԁ‫ۂ‬ઢͷςʔλؔ਺ͷཧ࿦ʢʹ [EtTh] ͷཧ࿦ʣ͕‫͛ڍ‬ΒΕ·͢ɻ(T5) ͔֬ʹɺIUTeich Λਅ໘໨ʹษ‫͢ڧ‬Ε͹‫ڀݚ‬࿦จͷʮ૿࢈ʯʹ‫͕ܨ‬Δ͜ͱΛࣄલʹอো͢Δ͜ͱ͸Ͱ͖·ͤΜ͕ɺ΋͠ʮࣗ෼ͷੜ‫ʹ׆‬௚઀໾ཱͭ΋ͷͰͳ͍‫ݶ‬Γɺؔ৺͕࣋ͯͳ͍ʯͱ͍͏ཧ۶ʹΑͬͯ IUTeich ͕ଟ͘ͷ਺࿦‫ز‬Կͷ‫ʹऀڀݚ‬ʮ‫س‬ආʯ͞Ε͍ͯΔͱ͢Ε͹ɺ
IUTeich ͷ਺࿦‫ز‬ԿશମͷதͰͷʮཱͪҐஔʯ͸७ਮ਺ֶͷਓؒࣾձશମͷதͰͷʮཱͪҐஔʯͷׄ޷ͷʮ૬ࣅ‫ܗ‬ͷϞσϧʯͱ͍͏͜ͱʹͳΓɺ͔͠΋ೋऀʢʹೋछྨͷʮཱͪҐஔʯʣͷྨࣅੑΛߟྀ͢Δͱɺ‫ऀޙ‬Λ‫͢ڀݚ‬Δ্ʹ͓͍ͯɺલऀͷ਼੎͸༗ҙٛͳࣔࠦΛ༩͑ΔՄೳੑΛൿΊ͍ͯΔͱ͍͏‫ํݟ‬΋Ͱ͖ΔͷͰ͸ͳ͍Ͱ͠ΐ͏͔ɻ࠷‫ʹޙ‬ɺIUTeich ͷ‫ؔʹڀݚ‬Θ͔ͬͯΒे਺೥ʹΘͨΓଟछଟ༷ͳߠఆతҙ‫ݟ‬΍൱ఆతҙ‫͓͖ͯͯ͠઀ʹݟ‬Γɺͦͷ‫͔ݧܦ‬Βੜ·Εͨ΋͏Ұͭͷ‫ײ‬૝ʹͳΓ·͕͢ɺཧ࿦ʹ͍ͭͯʮߠఆର൱ఆʯͱ͍͏ʮରཱ࣠ʯΛೝࣝͤ͞ΒΕΔ͜ͱ͸Ұ੾ͳ͍ͱ͸‫ͤ·͍ݴ‬Μ͕ɺͦͷʮ࣠ʯΑΓ΋ೡΖɺड़΂ΒΕ͍ͯΔҙ‫͕ݟ‬‫͔ͭີݫ‬ద੾ͳ਺ֶతཧղͷ্ʹ੒Γཱ͍ͬͯΔ΋ͷ͔Ͳ͏͔ͱ͍͏ʮ࣠ʯͦ͜ɺʮຊ໋ʯͰ͸ͳ͍͔ͱ‫ͤ͞͡ײ‬ΒΕΔ৔໘ʹ͠͹͠͹ૺ۰͠·͢ɻͨͩ͠ɺ‫Ͱ఺࣌ݱ‬͸ IUTeich ʹ͍ͭͯ͸ʮ‫͔ͭີݫ‬ద੾ͳ਺ֶతཧղͷ্ʹ੒Γཱ͍ͬͯΔʯ൱ఆతͳҙ‫ݟ‬Λड़΂ΒΕͨ৔໘͸‫ه‬Աʹ͋Γ·ͤΜɻߠఆɾ൱ఆΛ໰ΘͣɺIUTeich ʹ͍ͭͯ‫͔ͭີݫ‬ద੾ͳ਺ֶతཧղͷ্ʹ੒Γཱ͍ͬͯΔҙ‫ݟ‬Λ༗͢Δ‫ʹऀڀݚ‬ର͢Δఏ‫ʹͱ͜͏͍ͱݴ‬ͳΓ·͕͢ɺɹͦͷΑ͏ͳҙ‫ݟ‬͸ɺʢࢲΛ‫ؚ‬ΉʣୈࡾऀͰ΋‫͖Ͱূݕ‬ΔΑ͏ʹɺഎ‫͋ʹܠ‬Δ਺ֶతͳٞ࿦΍ࠜ‫ڌ‬౳ͱ‫ʹڞ‬ωοτ্Ͱʢ΋͘͠͸࠷௿Ͱ΋ஶऀͰ͋Δࢲʹରͯ͠ʣެ։͠ɺIUTeich ʹؔ͢Δɹ࿦఺ͷ੔ཧΛਤΔ౒ྗΛ͢΂͖࣌‫ʹظ‬ೖͬͨͷͰ͸ͳ͍͔ɺͱࢲ͸‫͓ͯ͡ײ͘ڧ‬Γ·͢ɻ10Ӊ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣ(8) ্ͷ (6), (7) Ͱղઆͨ͠ঢ়‫گ‬ΛҰ‫Ͱݴ‬૯‫ׅ͢‬Δͱɺ
IUTeich Λ८Δ‫׆‬ಈͷॏ৺͸ʮ‫ূݕ‬ʯ͔Βʮී‫ٴ‬ʯ΁ͱҠߦͭͭ͋͠Δ࣌‫͋ʹظ‬Δ͜ͱ͸‫͑ݴ‬ΔΑ͏ʹࢥ͍·͢ɻࠓ‫ޙ‬ɺʢ൒ੈ‫ل‬Ҏ্ʹ‫ٴ‬Ϳ๛෋ͳ࣮੷Λ࣋ͭʣ਺ཧ‫ݚ‬ͷ‫ڞ‬ಉར༻ࣄ‫ۀ‬Λ‫͢༻׆‬ΔΑ͏ͳ‫Ͱܗ‬ɺ਺ཧ‫ݚ‬Λ‫఺ڌ‬ʹͯ͠ࠃ಺֎ʹ޲͚ͯ IUTeich ʹؔ͢Δ৘ใൃ৴ɾී‫׆ٴ‬ಈ΁ͷऔΓ૊ΈΛߋʹ‫ڧ‬Խ͍͖͍ͯͨ͠ͱߟ͓͑ͯΓ·͢ɻւ֎Ͱ΋ʢৄ͍͠ঢ়‫͍ͯͭʹگ‬͸೺Ѳ͓ͯ͠Γ·ͤΜ͕ʣIUTeich ʹؔ͢Δηϛφʔ΍‫ूڀݚ‬ձ͕‫ا‬ը͞Εͯ͸ԿΒ͔ͷҙຯʹ͓͍ࣦͯഊʹऴΘΔɺͱ͍͏Α͏ͳ࿩Λ‫͓ͯ͠ʹࣖ͘ͳͱ౓ز‬Γ·͢ɻҰํɺ2015 ೥3 ݄ʹ༧ఆ͍ͯ͠Δ਺ཧ‫Ͱݚ‬ͷ‫ूڀݚ‬ձͷ‫ܭ‬ը·Ͱ૨͗ண͚Δ͜ͱ͕Ͱ͖ͨഎ‫ʹܠ‬͸ɺ΍͸Γ਺ཧ‫ʹݚ‬஝ੵ͞Ε͍ͯΔ༷ʑͳ‫ܗ‬ଶͷࣾձతɾจԽతΠϯϑϥʹΑΔॆ࣮ͨ͠αϙʔτମ੍͕͋Δ͜ͱΛɺࠓճͷใࠂΛవΊΔʹ౰ͨΓվΊͯ௧‫͓ͯ͠ײ‬Γ·͢ɻ2015 ೥ 3 ݄ͷ‫ूڀݚ‬ձ͸ͲͪΒ͔ͱ͍͑͹ɺࠃ಺ͷେֶӃੜ΍एखͷ‫ڀݚ‬ऀΛओͳର৅ͱͯ͠૝ఆ͍ͯ͠Δ΋ͷͰ͕͢ɺྫ͑͹ɺ਺ཧ‫ݚ‬ͷࠃࡍަྲྀࣄ‫Ͱۀ‬͸ɺຖ೥ւ֎͔Β 300ʙ400 ໊ఔͷ୹‫ظ‬ͷདྷ๚ऀɺͦΕ͔Β 10ʙ20 ໊ఔͷ௕‫ظ‬ʢʹ 1 έ݄Ҏ্ʣͷདྷ๚ऀ͕਺ཧ‫ݚ‬Λ๚໰͢Δ౳ɺւ֎ͷ‫ͱऀڀݚ‬ͷަྲྀ͕੝ΜʹߦͳΘΕ͓ͯΓ·͢ɻதʹ͸͜͜਺೥ͷ Saı̈di ࢯͷΑ͏ʹɺ٬һ‫ڭ‬तͱͯ͠ 3 έ݄Ҏ্଺ࡏ͢Δ‫͕ऀڀݚ‬ຖ೥
10 ໊ఔ͓Γ·͢ɻͨͩ͠ɺಛʹࠃࡍަྲྀʹ͍ͭͯ͸ԿΒ͔ͷ‫Ͱܗ‬ͷʮ‫੍ڧ‬ʯΛ‫͘ڧ‬ओு͢Δਓؒ΋૬౰਺ଘࡏ͢ΔΑ͏Ͱ͕͢ɺࢲ͸༷ʑͳ‫͔ݧܦ‬Βɺࠃ಺֎ͷަྲྀࣄ‫ۀ‬ͷ্ཱͪ͛ʹࡍ͠ɺ‫ۃڀ‬తͳਅ࣮Λ‫࢟ͳڏݠ‬੎Ͱ‫ۃݟ‬Ίɺ໌Β͔ʹ͢Δ͜ͱΛ࢖໋ͱ͢ΔҰछͷʮ‫ऀڀݚ‬ʯͷΑ͏ͳࢤͰɺࣄ‫ۀ‬ͷࢀՃऀͷຊԻͱ޲͖߹͍ɺ ͦͷຊ‫౓ؾ‬Λ‫ۃݟ‬Ίɺ͔ͬ͠Γ֬ೝͰ͖ͨ৔߹ʹͷΈࣄ‫ۀ‬Λ࣮ߦʹҠ͢ɹͱ͍͏࢟੎Λେ੾ʹ͢Δ͜ͱΛੲ͔Βઆ͍͓ͯΓ·͢ɻͦͷΑ͏ͳ࢟੎ʹ߆Δͷ͸ɺͦͷΑ͏ʹͯ͠ࢀՃऀͷʮຊ‫ؾ‬ʯΛ‫͢༻׆‬Δ͜ͱΛओମͱ͢Δަྲྀࣄ‫ʹۀ‬ͦ͜ɺʢͲΜͳʹաࠅͳฬଧͪΛ΋ͬͯͯ͠΋ʮ‫੍ڧ‬ʯͰ͸౸ఈ‫׎‬Θͳ͍ʂʣ௕‫ʹظ‬ΘͨΓ࣋ଓ͢Δ‫ؾ׆‬΍‫ྗ׆‬ɺʮ૬৐ޮՌʯ౳ɺਅʹ݈શͳల։
͕ੜ·ΕΔͱ֬৴͍ͯ͠Δ͔ΒͰ͢ɻ࣮ࡍɺྫ͑͹ɺ· ࢁԼࢯͱͷ IUTeich Λ८Δަྲྀͷ͖͔͚ͬͱͳͬͨͷ͸ɺຊਓ͔Βͷ 2012
೥ 9 ݄ࠒͷ࿈བྷʹΑΔɺIUTeich Λษ‫͏͍ͱ͍ͨ͠ڧ‬ਃ͠ग़ɺఏҊͰ͋Γɺͦͷ‫ޙ‬ͷαʔϕΠͷࣥචΛ‫ؚ‬Ί༷ͨʑͳ‫Ͱܗ‬ͷ‫׆ূݕ‬ಈ΋શͯ‫׬‬શʹຊਓʹΑΔఏҊͰ͋Γɺࢲ͔ΒͷʮൃҊʯ΍ʮґཔʯ౳͸Ұ੾͋Γ·ͤΜɻ· Saı̈di ࢯͷ৔߹ɺ2013 ೥ 7 ݄Ҏ߱ͷ IUTeich Λ८Δަྲྀ͸ɺ2013 ೥य़ࠒʹʢ௕೥ʹΘͨΓ Saı̈di ࢯͱ‫ڞ‬ಉ‫ڀݚ‬Λߦͳ͍ͬͯΔ‫ۄ‬઒ࢯ‫ܦ‬༝Ͱʣ൒೥Ӊ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 12 ݄‫ࡏݱ‬ʣ11ఔલ͔Β Saı̈di ࢯ͕ʢࢲͱ͸‫׬‬શʹؔ܎ͷͳ͍‫ࣗ͝Ͱܗ‬෼ͷҙࢥʹΑΓʂʣ
[FrdI] ౳ɺIUTeich ͷษ‫ڧ‬Λ໨ඪʹɺʮ४උͷ࿦จʯͷษ‫ʹڧ‬ணखͨ͜͠ͱΛ஌ͬͨ͜ͱ͕͖͔͚ͬͰͨ͠ɻ· ੕ࢯͷ৔߹ɺҎલ͔ΒೋਓͰߦͳ͍ͬͯΔηϛφʔͰ IUTeich ΛऔΓ্͛Δʹࢸͬͨͷ͸ɺࢲ͕੕ࢯͱ௕೥ʹΘͨΓࢦಋ‫ڭ‬һ΍‫ڞ‬ಉ‫ͯ͠ͱऀڀݚ‬ଟछଟ༷ͳԕΞʔϕϧ‫ز‬Կؔ࿈ͷ࿩୊Λ୊ࡐʹ੝Μʹަྲྀ͖ͯͨ͜͠ͱ͕എ‫͋ʹܠ‬Γ·͕͢ɺͦͷ௕೥ͷަྲྀ΋ɺ੕ࢯֶ͕෦ੜͷࠒʹʢࢲͱ͸‫׬‬શʹؔ܎ͷͳ͍‫ࣗ͝Ͱܗ‬෼ͷҙࢥʹΑΓʂʣࢲͷ࿦จʢ[pGC]ʣͷ͋Δ෦෼ΛಡΜͰɺ͋Δఔ౓ཧղ͠ɺp ਐηΫγϣϯ༧૝౳ɺp ਐԕΞʔϕϧ‫ز‬ԿΛษ‫͢ڧ‬ΔͨΊʹࢲΛʢम࢜՝ఔͷʣࢦಋ‫ڭ‬һʹࢤ๬ͯ͠Լͬͨ͜͞ͱ͕͖͔͚ͬͰͨ͠ɻͳ͓ɺ͜ͷ 3 ໊ͷ৔߹ɺࢲ͕༷ʑͳ࿦จΛࣥචͨ͠Γɺͦͷؔ࿈ͷ‫ڀݚ‬Λͨ͠Γ͢Δ͜ͱʹΑ๊ͬͯ͘ʹࢸͬͨ‫ײ‬૝Ͱɺ࿦จ౳ʹ͸໌ࣔతʹ‫͔ͨͬͳ͠ࡌه‬΋ͷͰ΋ɺࢲ͔Βͷࢦఠ΍‫ٴݴ‬౳Λ଴ͭ·Ͱ΋ͳ͘ɺࣗ෼ࣗ਎ͷʮಠཱͳ‫࡯؍‬ʯͱͯ͠ಉ༷ͳ಺༰ͷ‫ײ‬૝Λड़΂ΒΕͨ͜ͱ͸Ұճ΍ೋճͰ͸ͳ͘ɺͪ͜ΒͰ΋͖֮͑Εͳ͍΄Ͳͷճ਺͋Γɺͦͷ౓ʹେม‫ײ‬ಈ͓ͯ͠Γ·͢ɻ͜ͷΑ͏ͳޮՌ͸ຊਓͷԢ੝ͳҙཉͷ্ʹ੒Γཱ͍ͬͯΔ‫׆‬ಈͰͳ͍ͱ࣮‫͢ݱ‬Δ΋ͷͰ͸͋Γ·ͤΜɻ(9) ʮத֩తͳ 3 ໊ʯͷࢁԼࢯɺSaı̈di ࢯɺ੕ࢯΛ࢝Ίɺ͝ଟ๩ͳதɺ‫و‬ॏͳ͓࣌ؒΛʢ৔߹ʹΑͬͯ͸େྔʹʣׂ͍ͯࠓճͷใࠂͰղઆ༷ͨ͠ʑͳ‫׆‬ಈʹଟେͳߩ‫ݙ‬Λͯ͠Լͬͨؔ͞܎ऀͷօ༷ͷ֨ผͳΔ͝೤ҙͱ͝‫ྱ͓͘ਂʹྗڠ‬Λਃ্͛͠·͢ɻจ‫ݙ‬Ϧετ[Qp GC] S. Mochizuki, A Version of the Grothendieck Conjecture for p-adic LocalFields, 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, Proceedingsof 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.

12Ӊ஦ࡍλΠώϛϡʔϥʔཧ࿦ͷ‫ূݕ‬ɿਐ௙ঢ়‫گ‬ͷใࠂʢ2014 ೥ 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 Étale 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 Teichmüller Theory I: Construction of HodgeTheaters, RIMS Preprint 1756 (August 2012).
[IUTchII] S. Mochizuki, Inter-universal Teichmüller Theory II: Hodge-Arakelov-theoretic
Evaluation, RIMS Preprint 1757 (August 2012).
[IUTchIII] S. Mochizuki, Inter-universal Teichmüller Theory III: Canonical Splittings ofthe Log-theta-lattice, RIMS Preprint 1758 (August 2012).
[IUTchIV] S. Mochizuki, Inter-universal Teichmüller Theory IV: Log-volume Computations and Set-theoretic Foundations, RIMS Preprint 1759 (August 2012).
[Pano] S. Mochizuki, A Panoramic Overview of Inter-universal Teichmüller Theory,Algebraic number theory and related topics 2012, RIMS Kōkyūroku Bessatsu
B51, Res. Inst. Math. Sci. (RIMS), Kyoto (2014), pp. 301-345.