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Abstract des Vortrages von Alexander Molnar

Arithmetic and intermediate Jacobians of some rigid Calabi-Yau threefolds

Generalizing the Jacobian variety of a curve, one may associate to any higher dimensional complex variety X, some complex varieties defined in terms of cohomological quotients of X, the intermediate Jacobians of X. These receive cycle class maps, so there is much interest in being able to study them over number fields, in order to study the many open conjectures on cycles and Chow groups of varieties. We will discuss some examples of rigid Calabi-Yau threefolds where we compute the intermediate Jacobians as complex tori, and show that each choice of rational model of the threefolds leads to a natural rational model of the intermediate Jacobians. This allows us to consider (quadratic) twists of the threefolds, see how this affects the 'twisted' intermediate Jacobians, and compute the respective L-functions looking for relationships between them.