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Colloquium
Seminar information archive ～12/08｜Next seminar｜Future seminars 12/09～
| Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
|---|---|
| URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium_e/index_e.html |
2011/12/16
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
TAKAGI, Shunsuke (Graduate School of Mathematical Sciences, University of Tokyo)
Application of positive characteristic methods to singularity theory (JAPANESE)
TAKAGI, Shunsuke (Graduate School of Mathematical Sciences, University of Tokyo)
Application of positive characteristic methods to singularity theory (JAPANESE)
[ Abstract ]
As an application of positive characteristic methods to singularity theory, I will talk about a characterization of singularities in characteristic zero using Frobenius maps. Log canonical singularities form a class of singularities associated to the minimal model program. It is conjectured that they correspond to $F$-pure singularities, which form a class of singularities defined via splitting of Frobenius maps. In this talk, I will explain a recent progress on this conjecture, especially its connection to another conjecture on ordinary reductions of Calabi-Yau varieties defined over number fields.
As an application of positive characteristic methods to singularity theory, I will talk about a characterization of singularities in characteristic zero using Frobenius maps. Log canonical singularities form a class of singularities associated to the minimal model program. It is conjectured that they correspond to $F$-pure singularities, which form a class of singularities defined via splitting of Frobenius maps. In this talk, I will explain a recent progress on this conjecture, especially its connection to another conjecture on ordinary reductions of Calabi-Yau varieties defined over number fields.
