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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 |
2025年04月25日(金)
13:30-15:00 数理科学研究科棟(駒場) 118号室
河上龍郎 氏 (東京大学)
Higher F-injective singularities
河上龍郎 氏 (東京大学)
Higher F-injective singularities
[ 講演概要 ]
The theory of F-singularities is a field that studies singularities in positive characteristic defined via the Frobenius morphism. A particularly well-known aspect of the theory is its correspondence, via reduction, with singularities that appear in birational geometry in characteristic zero.
In recent years, higher versions of such singularities in characteristic zero--such as higher Du Bois singularities--have been actively studied. In this talk, I will discuss how a higher analogue of F-singularity theory can be developed in positive characteristic by using the Cartier operator, which serves as a higher version of the Frobenius morphism.
In particular, I will introduce higher F-injective singularities, which correspond to higher Du Bois singularities, and focus on how the correspondence via reduction can be established.
This is joint work with Jakub Witaszek.
The theory of F-singularities is a field that studies singularities in positive characteristic defined via the Frobenius morphism. A particularly well-known aspect of the theory is its correspondence, via reduction, with singularities that appear in birational geometry in characteristic zero.
In recent years, higher versions of such singularities in characteristic zero--such as higher Du Bois singularities--have been actively studied. In this talk, I will discuss how a higher analogue of F-singularity theory can be developed in positive characteristic by using the Cartier operator, which serves as a higher version of the Frobenius morphism.
In particular, I will introduce higher F-injective singularities, which correspond to higher Du Bois singularities, and focus on how the correspondence via reduction can be established.
This is joint work with Jakub Witaszek.
