12
ӉλΠώϛϡʔϥʔཧͷݕɿਐঢ়گͷใʢ2014 12 ࡏݱʣ ژେཧղੳڀݚॴɾڭतɹ৽Ұ ɹ 2012 8 ʹӉλΠώϛϡʔϥʔཧʢIUTeichʣʹΔ࿈ଓจΛ දɺ2013 12 ɺཧͷݕʹ࿈׆ಈʹΔΛ։·ɺ ͷޙͷ 1 ͷʹʑͳ৽ల։Γ·ͷͰվΊใ·ɻɹ (1) 2014 ʹߦͳɺIUTeich ʹΔޱ಄දͷ 2 ʹͳΓ·ɿ 2014 02 20 ʢ2 ʴ 2 ɺ ژେཧղੳڀݚॴͷηϛφʔʣɺ 2014 05 24 ʢ2 ʴ 2 ɺ۽ຊେʣɻ ͷߨԋͷϨΫνϟʔϊʔτΕ·Ͱͷ IUTeich ࿈ͷߨԋͷͷΛগमਖ਼ɾ ՃචͷͰɺΕ·ͰͱൺଟগΊʹऔΒߨԋΛ ׆༻ΑΓͳղઆௌͷͷରԠͰ·ɻϨΫνϟʔϊʔτ ͷޙʑमਖ਼Γɺ ৽൛ʢಉͳ༰ΛղઆαʔϕΠʢ[Pano]ʣͱ ʹڞʣͷΤϒαΠτͰ։Γ·ɻ2 ͷߨԋओʹཧݚͷେӃੜ ͱϙετυΫͷएखɺΕΒੲΒͷηϛφʔʹՃΔࡏݍͷ ڀݚͷߨԋͰɺՃͷਓ 10ʙ20 ਓఔͰɻҰɺ5 ͷߨԋ۽ͷՃ౻จڭݩͷটͰݱͷͰɺՃभେɺभͷ ݚڀଟɺਓ 40ʙ50 ਓఔͰɻճͷটͷഎʹܠɺ2005 7 ʙ2011 3 ͷɺՃ౻ژڭͷ।ڭतΛΒΕɺ 2ʙ3 िʹ 1 ճʢʹ 3ʙ4 ఔʣɺ 2 ਓͰߦͳ IUTeich ͷηϛφʔΓ·ɻɺIUTeich ·ల ͷஈ֊ʹΘͰɺଟͷ߹Λ๓ԆʑͱΓΔͷ૬खΛ ԼՃ౻ʹࢯେมײகΓ·ɻ (2) Լ߶ʢژେཧղੳڀݚॴཧղੳڀݚηϯλʔಛࢣߨʣͱ 2012 10 ҎɺIUTeich ʹΔηϛφʔΛߦͳΓ·ɺ2014 ɺ 3 िʹ 1 ճʢʹ 4ʙ5 ఔʣɺ IUTeich ʹΔηϛφʔΛߦͳ·ɻΕ·Ͱ௨Γ IUTeich ͷʑͳज़త ͳଆ໘ʹɺԼΒज़తͳఠʢʹ 2014 ɺඦ 2013 ΑΓେ෯ʹݮ 30 ఔʣΛ౿·จΛमਖ਼ɺमਖ਼൛Λ ͷΤϒαΠτͰ։·ɻԼ 2013 Β IUTeich ʢཧʹඞཁ

N G ¶: g rs Z t ~ $ y l D ýmotizuki/IUTeich Kenshou Houkoku 2014-1… · ¯ ` z2013 å12 D z g æ w U Â t È ` h Æ t b C ¬ ` ` h U z ... C ` b { y (1) 2014 å t æ s l h zIUTeich

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Page 1: N G ¶: g rs Z t ~ $ y l D ýmotizuki/IUTeich Kenshou Houkoku 2014-1… · ¯ ` z2013 å12 D z g æ w U Â t È ` h Æ t b C ¬ ` ` h U z ... C ` b { y (1) 2014 å t æ s l h zIUTeich

2014 12

2012 8 IUTeich2013 12

1

(1) 2014 IUTeich 2

2014 02 20 2 2

2014 05 24 2 2

IUTeich

[Pano]2

10 20 5

40 50 2005 7 20113

2 3 1 3 4

2 IUTeich IUTeich

(2)2012 10 IUTeich 2014

3 1 4 5

IUTeich IUTeich2014

2013 302013 IUTeich

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2 2014 12

4 3200 300

1

2014 09 16 19 4 1 5

IUTeich [AbsTopIII]

IUTeich

10

2015 03 09 20 10 1 7

RIMSRIMS

(3) Mohamed Saıdi

2014 06 25 09 24

[IUTchI], [IUTchII], [IUTchIII] 32013

70

1 2 3 9

20132013

2013 Saıdi

IUTeich

IUTeich

[IUTchI], [IUTchII]

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2014 12 3

· [SemiAnbd], §1, §2, §3, §5, §6;· [FrdI]; [FrdII], §1, §2, §3;· [EtTh] ;· [AbsTopI], §1, §4; [AbsTopII], §3; [AbsTopIII], §1, §2

[IUTchIII], [IUTchIV]

· [AbsTopIII], §3, §4, §5;· [GenEll]

(4)2014 IUTeich

2 1 3

2013[SemiAnbd], [AbsTopI], [AbsTopII], [AbsTopIII]

[AbsTopIII]mono-anabelian geometry

2015 3IUTeich [HASurI], [HASurII], [FrdI],

[FrdII], [EtTh], [GenEll] 2014 1 3 2014 44

4 [IUTchIV] IUTeich1 3 [IUTchI], [IUTchII], [IUTchIII]

52013 5 11 140

5100

10 15

2014 2 1IUTeich

40

Page 4: N G ¶: g rs Z t ~ $ y l D ýmotizuki/IUTeich Kenshou Houkoku 2014-1… · ¯ ` z2013 å12 D z g æ w U Â t È ` h Æ t b C ¬ ` ` h U z ... C ` b { y (1) 2014 å t æ s l h zIUTeich

4 2014 12

Saıdi

Kummer

IUTeich

IUTeich

(5) Chung Pang Mok 201410 11 IUTeich

Mok 102015 3

Mok

(6) (2), (3), (4) 33 IUTeich

3Saıdi 40 30

30 10 2004Hartshorne

10 IUTeich

10 IUTeich 20

310

Saıdi

p pSaıdi (3), (4)

Page 5: N G ¶: g rs Z t ~ $ y l D ýmotizuki/IUTeich Kenshou Houkoku 2014-1… · ¯ ` z2013 å12 D z g æ w U Â t È ` h Æ t b C ¬ ` ` h U z ... C ` b { y (1) 2014 å t æ s l h zIUTeich

2014 12 5

1 3 [IUTchI],[IUTchII], [IUTchIII] 4

[IUTchIV] ABC Hodge-Arakelov

1 3 43 2013 12 (2),

(3), (4) 3

32014 32013IUTeich

IUTeich Saıdi 3 35

3 IUTeich

20

3

3

canonicality

ABC

Page 6: N G ¶: g rs Z t ~ $ y l D ýmotizuki/IUTeich Kenshou Houkoku 2014-1… · ¯ ` z2013 å12 D z g æ w U Â t È ` h Æ t b C ¬ ` ` h U z ... C ` b { y (1) 2014 å t æ s l h zIUTeich

6 2014 12

IUTeich

20 30

2010 10 20128 10 2010

(7) (6)

(2)IUTeichHodge-Arakelov

IUTeich

(3), (4)

Page 7: N G ¶: g rs Z t ~ $ y l D ýmotizuki/IUTeich Kenshou Houkoku 2014-1… · ¯ ` z2013 å12 D z g æ w U Â t È ` h Æ t b C ¬ ` ` h U z ... C ` b { y (1) 2014 å t æ s l h zIUTeich

2014 12 7

Saıdi 2013 5 11

IUTeich

IUTeich2012 8

IUTeich

IUTeich

(2), (3), (4), (6) 3IUTeich

3

(H1) IUTeich1500 2500

(H2) IUTeich

(H3)IUTeich

Page 8: N G ¶: g rs Z t ~ $ y l D ýmotizuki/IUTeich Kenshou Houkoku 2014-1… · ¯ ` z2013 å12 D z g æ w U Â t È ` h Æ t b C ¬ ` ` h U z ... C ` b { y (1) 2014 å t æ s l h zIUTeich

8 2014 12

(H4) Wiles 1995

IUTeich

Wiles (H3)

(H5)20

30

(H1) (H5) (H1) (H2) (H3) (H4)(H4) (H5)

(T1)Weil 1960

EGA SGA

(T2)[QpGC] 8

(4) (6)

(T3)

Page 9: N G ¶: g rs Z t ~ $ y l D ýmotizuki/IUTeich Kenshou Houkoku 2014-1… · ¯ ` z2013 å12 D z g æ w U Â t È ` h Æ t b C ¬ ` ` h U z ... C ` b { y (1) 2014 å t æ s l h zIUTeich

2014 12 9

(T4) IUTeichIUTeich

Faltings 1983Faltings

IUTeich

[EtTh]

(T5) IUTeich

IUTeich

IUTeich

IUTeich

IUTeich

IUTeich

IUTeich

Page 10: N G ¶: g rs Z t ~ $ y l D ýmotizuki/IUTeich Kenshou Houkoku 2014-1… · ¯ ` z2013 å12 D z g æ w U Â t È ` h Æ t b C ¬ ` ` h U z ... C ` b { y (1) 2014 å t æ s l h zIUTeich

10 2014 12

(8) (6), (7)

IUTeich

IUTeich

IUTeich2015

3

2015 3

300 40010 20 1

Saıdi 310

· IUTeich 20129 IUTeich

· Saıdi 2013 7 IUTeich 2013Saıdi

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2014 12 11

Saıdi[FrdI] IUTeich

· IUTeich

[pGC]p p

3

(9) 3 Saıdi

[QpGC] 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.

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12 2014 12

[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, KyushuJ. 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.

[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: DecompositionGroups and Endomorphisms, J. Math. Sci. Univ. Tokyo 20 (2013), pp. 171-269.

[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. OkayamaUniv. 52 (2010), pp. 1-28.

[IUTchI] S. Mochizuki, Inter-universal Teichmuller Theory I: Construction of HodgeTheaters, RIMS Preprint 1756 (August 2012).

[IUTchII] S. Mochizuki, Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoreticEvaluation, RIMS Preprint 1757 (August 2012).

[IUTchIII] S. Mochizuki, Inter-universal Teichmuller Theory III: Canonical Splittings ofthe Log-theta-lattice, RIMS Preprint 1758 (August 2012).

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

[Pano] S. Mochizuki, A Panoramic Overview of Inter-universal Teichmuller Theory,Algebraic number theory and related topics 2012, RIMS Kokyuroku BessatsuB51, Res. Inst. Math. Sci. (RIMS), Kyoto (2014), pp. 301-345.