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パーフェクトイド空間とコホモロジー

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Avatar for Naoya Umezaki Naoya Umezaki
October 06, 2018
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 パーフェクトイド空間とコホモロジー

MATHPOWER2018での講演。フィールズ賞受賞者Peter Scholzeの業績紹介。

Avatar for Naoya Umezaki

Naoya Umezaki

October 06, 2018
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  1. pਐ਺ ▶ ࣮਺Ͱ͸0.9999 · · · = 1 ▶ p

    = 2ͷͱ͖ɺpਐ਺Ͱ͸· · · 111111 = −1
  2. ύʔϑΣΫτΠυۭؒ ▶ ୅਺زԿ͸ଟ߲ࣜx, x2 + ax + b, . .

    . ▶ ղੳزԿ͸ऩଋႈڃ਺x + px + p2x2 + · · · ▶ ύʔϑΣΫτΠυۭؒ͸ 1/x + p + p2x + · · · , 1/xp + 1 + px + · · · , 1/xp2 + 1/xp + · · · , . . .
  3. 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