Date | 2018-04-06 |
---|---|

Speaker | 김태경 |

Dept. | IBS-CGP |

Room | 129-104 |

Time | 13:00-14:00 |

Abstract: In the groundbreaking and straightforward-titled 1985 paper “Il n’y a pas de variété abélienne sur Z” (“There are no abelian schemes over Z”), Fontaine studied the ramification of the p^n-torsion group A

$${p}^{n}$$
of an abelian variety A defined over certain “smaller” number fields, having everywhere good reduction. The upshot is, such a group scheme A

$${p}^{n}$$
is mildly ramified, so mild that NO such group schemes exist. As a consequence, he showed that there is no abelian varieties over Q having everywhere good reduction. In this talk, I will give essential underlying ideas in the proof of such results. Recent generalization of Schoof will be also introduced.

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