Humboldt Universität zu Berlin
Mathem.-Naturwissenschaftliche Fakultät
Institut für Mathematik

Forschungsseminar "Arithmetische Geometrie"

Sommersemester 2017

Das Forschungsseminar findet dienstags in der Zeit von 13:15 - 15:00 Uhr in der Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 3.006 (Haus 3, Erdgeschoss), statt.

Wegen Forschungsfreisemester wird das Forschungsseminar in diesem Semester nur an ausgewählten Terminen stattfinden.
Weitere Informationen werden in nächster Zeit hier bekanntgegeben.

18.07.2017 Charles Vial (Universität Bielefeld)
Title: Distinguished models of intermediate Jacobians
Abstract: Let X be a smooth projective variety defined over a subfield K of the complex numbers. It is natural to ask whether the complex abelian variety that is the image of the Abel-Jacobi map defined on algebraically trivial cycles admits a model over K. I will show that it admits a unique model making the Abel-Jacobi map equivariant with respect to the action of the automorphism group of the complex numbers fixing K. We offer three applications. First, we show that such a model is a derived-invariant for smooth projective varieties defined over K. Second, we answer a question of Mazur by showing that this model over the base field K is dominated by the Albanese variety of a product of components of the Hilbert scheme of X. Third, we recover a result of Deligne on complete intersections of Hodge level one. This is joint work with Jeff Achter and Yano Casalaina-Martin.


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