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We obtain examples of smooth projective varieties over ${\mathbb C}$ that violate the integral Hodge conjecture and for which the total Chow group is of finite rank. Moreover, we show that there exist such examples defined over number fields.

We present another example of a 3-variable polynomial defining a $K3$-hypersurface and having a logarithmic Mahler measure expressed in terms of a Dirichlet $L$-series.

In this paper, we construct abelian varieties associated to Gauss’ and Appell–Lauricella hypergeometric series. Abelian varieties of this kind and the algebraic curves we define to construct them were considered by several authors in settings ranging from monodromy groups (Deligne, Mostow), exceptional sets (Cohen, Wolfart, Wüstholz), modular embeddings (Cohen, Wolfart) to CM-type (Cohen, Shiga, Wolfart) and modularity (Darmon). Our contribution is to provide a complete, explicit and self-contained geometric construction.

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On the integral Hodge conjecture for varieties with trivial Chow group

A Mahler Measure of a K3 Surface Expressed as a Dirichlet L-Series

Hypergeometric Abelian Varieties

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3 results

On the integral Hodge conjecture for varieties with trivial Chow group

A Mahler Measure of a K3 Surface Expressed as a Dirichlet L-Series

Hypergeometric Abelian Varieties