JOINT IAS/PU NUMBER THEORY SEMINAR | |

Topic: | Constructing Abelian Varieties over Qbar Not Isogenous to a Jacobian |

Speaker: | Jacob Tsimerman |

Affiliation: | Prirnceton University |

Date: | Thursday, October 28 |

Time/Room: | 4:30pm - 5:30pm/Fine Hall -- 214 |

We discuss the following question of Nick Katz and Frans Oort: Given an Algebraically closed field K , is there an Abelian variety over K of dimension g which is not isogenous to a Jacobian? For K the complex numbers its easy to see that the answer is yes for g>3 using measure theory, but over a countable field like Qbar new methods are required. Building on work of Chai-Oort, we show that, as expected, such Abelian varieties exist for K=Qbar and g>3 . We will explain the proof as well as its connection to the Andre Oort conjecture.