Tweet
Tweet

Slide 1

Slide 1 text

ύʔϑΣΫτΠυۭؒͱ ίϗϞϩδʔ Peter Scholzeͷۀ੷঺հ ക࡚௚໵@unaoya ͢͏͕͘ͿΜ͔ MATHPOWER2018 10/6

Slide 2

Slide 2 text

ड৆ཧ༝ p ਐ਺Ͱͷ୅਺زԿͷݚڀ ▶ ύʔϑΣΫτΠυۭؒͷཧ࿦ ▶ ϥϯάϥϯζରԠ΁ͷԠ༻ ▶ ৽͍͠ίϗϞϩδʔཧ࿦

Slide 3

Slide 3 text

pਐ਺ ༗ཧ਺͔Β࣮਺΁3.14159265 · · · ༗ཧ਺͔Βp ਐ਺΁ · · · 245123 = 3+2p+1p2 +5p3 +4p4 +2p5 +· · ·

Slide 4

Slide 4 text

pਐ਺ ▶ ࣮਺Ͱ͸0.9999 · · · = 1 ▶ p = 2ͷͱ͖ɺpਐ਺Ͱ͸· · · 111111 = −1

Slide 5

Slide 5 text

୅਺زԿֶ ଟ߲ࣜΛߟ͑Δͱਤܗ͕ܾ·Δɻ ▶ ԁx2 + y2 = 1 ▶ ପԁۂઢy2 = x3 + x ▶ ϑΣϧϚʔۂઢxn + yn = 1

Slide 6

Slide 6 text

ίϗϞϩδʔ ݀ͷ਺Λ਺͑Δɻਤܗͷ෼ྨ͕Ͱ͖Δɻ H1 sing (X) = H1 dR (X) = R2

Slide 7

Slide 7 text

ίϗϞϩδʔ ༷ʑͳίϗϞϩδʔ͕͋Δɻ υϥʔϜ ίϗϞϩδʔ ಛҟ ίϗϞϩδʔ ؔ਺΍ ඍ෼ํఔࣜ ۭؒͷதͷ ਤܗͷมܗ

Slide 8

Slide 8 text

ίϗϞϩδʔͷൺֱ υϥʔϜ ίϗϞϩδʔ ಛҟ ίϗϞϩδʔ ϗοδ ίϗϞϩδʔ ίϗϞϩδʔͷൺֱ͔Βपظ͕ग़ͯ͘Δɻ

Slide 9

Slide 9 text

੔਺࿦ͱίϗϞϩδʔ ▶ ੲ͔Βߟ͑ΒΕ͍͍ͯͨΖΜͳ໰୊͕ί ϗϞϩδʔΛ࢖ͬͯදݱͰ͖Δɻ ▶ ੔਺࿦ʹ΋Ԡ༻ʢϦʔϚϯ༧૝ͷྨࣅʣ ▶ ίϗϞϩδʔΛௐ΂Ε͹৭ʑΘ͔Δʂ

Slide 10

Slide 10 text

ύʔϑΣΫτΠυۭؒ ▶ ୅਺زԿ͸ଟ߲ࣜx, x2 + ax + b, . . . ▶ ղੳزԿ͸ऩଋႈڃ਺x + px + p2x2 + · · · ▶ ύʔϑΣΫτΠυۭؒ͸ 1/x + p + p2x + · · · , 1/xp + 1 + px + · · · , 1/xp2 + 1/xp + · · · , . . .

Slide 11

Slide 11 text

ύʔϑΣΫτΠυۭؒ ύʔϑΣΫτΠυۭؒΛ࢖͏ͱίϗϞϩδʔ ͕ௐ΂΍͘͢ͳΔɻ

Slide 12

Slide 12 text

pਐHodgeཧ࿦ ίϗϞϩδʔͷൺֱఆཧ Hi ´ et (X, Fp ) ⊗ OC /p ∼ = Hi ´ et (X, O+ X /p) Hi ´ et (X, Qp ) ⊗Qp BdR ∼ = Hi dR (X0 ) ⊗k BdR

Slide 13

Slide 13 text

pਐपظࣸ૾ ϗοδཧ࿦ͷp ਐ൛ πHT : S∗ Kp → F ପԁۂઢͷ ϞδϡϥΠ ίϗϞϩδʔ ͷൺֱ

Slide 14

Slide 14 text

LanglandsରԠ ΨϩΞදݱ อܕදݱ ପԁۂઢ อܕܗࣜ ▶ ࠨ޲͖ɿΨϩΞදݱͷߏ੒ ΞΠώϥʔ-ࢤଜ etc ▶ ӈ޲͖ɿΨϩΞදݱͷอܕੑ ςΠϥʔ-ϫΠϧζ etc

Slide 15

Slide 15 text

LanglandsରԠ ΨϩΞදݱ อܕදݱ 1. ίϗϞϩδʔͷൺֱఆཧ 2. ہॴରশۭؒͷp-torsionίϗϞϩδʔ͕ ௐ΂ΒΕΔ 3. ΑΓ޿͍อܕදݱ͔ΒΨϩΞදݱͷߏ੒ 4. ΨϩΞදݱͷอܕੑʹ΋Ԡ༻

Slide 16

Slide 16 text

৽͍͠ίϗϞϩδʔཧ࿦ ίϗϞϩδʔΛ౷Ұతʹѻ͍͍ͨ ʁ Τλʔϧ ΫϦε λϦϯ υϥʔϜ

Slide 17

Slide 17 text

৽͍͠ίϗϞϩδʔཧ࿦ ϥϯάϥϯζରԠͷݚڀ͔Β γτΡΧʁ Τλʔϧ ΫϦε λϦϯ υϥʔϜ