とおき，さらに
Fil1M(M) :={x∈ M(M)|(idS⊗(1⊗ϕ))(x)∈(Fil1S)⊗SM⊂S⊗SM}
とおく．またM(M)にもFrobeniusが誘導される．
定理 B.6（[Kis10, 1.4.2]） p > 2とする．OL 上のp 可除群G に対しM(G) :=
M(TpG∨(−1))*38，D(G) :=D(G ⊗OLk)とおく．このときMはOL上のp可除群 のなす圏とBTϕ/Sとの圏同値を誘導する．また自然なフィルトレーションを保つϕ 同変な同型
D(G)(S)−→ M∼= (M(G))
が存在する．特に環準同型S →W;u 7→0でさらに係数拡大することによりϕ同変 な同型
D(G)(W)−→∼= ϕ∗(M(G)/uM(G))
を得る．
注意 B.7 定理B.6はp = 2 でも成り立つことが知られている．[Kim12, Lau14, Lau19, Liu13]および[IIK18, §11.4]を参照せよ．
謝辞 本稿は2015年度整数論サマースクール「志村多様体とその応用」における筆 者の講演「志村多様体の整モデル」に基づいている．原稿にコメントを下さった伊藤 哲史氏，越川皓永氏，時本一樹氏，松本雄也氏に感謝する．なお本稿の最終校正は筆 者がInstitute for Advanced Studyに所属している間に行われた．その際に筆者は National Science Foundationの研究費DMS-1638352から支援を受けている．
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