Humboldt Universität zu Berlin
Mathem.-Naturwissenschaftliche Fakultät
Institut für Mathematik
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.
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. |
Wintersemester 2007/08
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