Roberto Laface (TU München)
Tuesday, May 22, 2018 - 13:15
HU, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin-Adlershof, 3.006, Erdgeschoss
Forschungsseminar "Arithmetische Geometrie"
Prof. Dr. Jürg Kramer, Prof. Dr. Thomas Krämer
I will talk about the Picard numbers of abelian varieties over C (joint work with Klaus Hulek) and over fields of positive characteristic. After providing an algorithm for computing the Picard number, we show that the set Rg of Picard numbers of g-dimensional abelian varieties is not complete if g ≥ 2, that is there esist gaps in the sequence of Picard numbers seen as a sequence of integers. We will also study which Picard numbers can or cannot occur, and we will deduce structure results for abelian varieties with large Picard number. In characteristic zero we are able to give a complete and satisfactory description of the overall picture, while in positive characteristic there are several pathologies and open questions yet to be answered.
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