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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 Hn\dR(Y/X) at x, i.e. the largest i such that the line of the conjugate filtration is contained in Fili of the Hodge filtration. For every triple (G,μ,r) consisting of a connected, reductive Fp-group G, a cocharacter μ∈X∗(G) and an Fp-representation r of G, we state a generalized Ogus Principle. If ζ:X→\GZipμ 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 Hn\dR(Y/X) at x, i.e. the largest i such that the line of the conjugate filtration is contained in Fili of the Hodge filtration. For every triple (G,μ,r) consisting of a connected, reductive Fp-group G, a cocharacter μ∈X∗(G) and an Fp-representation r of G, we state a generalized Ogus Principle. If ζ:X→\GZipμ 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.
