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| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) 118号室 |
|---|---|
| 担当者 | 權業 善範、河上 龍郎 、榎園 誠 |
2024年07月04日(木)
13:00-14:30 数理科学研究科棟(駒場) ハイブリッド開催/118号室
Stefan Reppen 氏 (東京大学)
On a principle of Ogus: the Hasse invariant's order of vanishing and "Frobenius and the Hodge filtration'' (English)
Stefan Reppen 氏 (東京大学)
On a principle of Ogus: the Hasse invariant's order of vanishing and "Frobenius and the Hodge filtration'' (English)
[ 講演概要 ]
In joint work with W. Goldring we generalize a result of Ogus that, under certain technical conditions, the vanishing order of the Hasse invariant of a family $Y/X$ of $n$-dimensional Calabi-Yau varieties in characteristic $p$ at a point $x$ of $X$ equals the "conjugate line position" of $H^n_{\dR}(Y/X)$ at $x$, i.e. the largest $i$ such that the line of the conjugate filtration is contained in $\text{Fil}^i$ of the Hodge filtration. For every triple $(G,\mu,r)$ consisting of a connected, reductive $\mathbb{F}_p$-group $G$, a cocharacter $\mu \in X_*(G)$ and an $\mathbb{F}_p$-representation $r$ of $G$, we state a generalized Ogus Principle. If $\zeta:X \to \GZip^{\mu}$ is a smooth morphism, then the group theoretic Ogus Principle implies an Ogus Principle on $X$. We deduce an Ogus Principle for several Hodge and abelian-type Shimura varieties and the moduli space of K3 surfaces. In the talk I will present this work.
In joint work with W. Goldring we generalize a result of Ogus that, under certain technical conditions, the vanishing order of the Hasse invariant of a family $Y/X$ of $n$-dimensional Calabi-Yau varieties in characteristic $p$ at a point $x$ of $X$ equals the "conjugate line position" of $H^n_{\dR}(Y/X)$ at $x$, i.e. the largest $i$ such that the line of the conjugate filtration is contained in $\text{Fil}^i$ of the Hodge filtration. For every triple $(G,\mu,r)$ consisting of a connected, reductive $\mathbb{F}_p$-group $G$, a cocharacter $\mu \in X_*(G)$ and an $\mathbb{F}_p$-representation $r$ of $G$, we state a generalized Ogus Principle. If $\zeta:X \to \GZip^{\mu}$ is a smooth morphism, then the group theoretic Ogus Principle implies an Ogus Principle on $X$. We deduce an Ogus Principle for several Hodge and abelian-type Shimura varieties and the moduli space of K3 surfaces. In the talk I will present this work.
