RÉSUMÉ

Elliptic curves are the dimension one Calabi-Yau varieties. The modularity conjecture has been established for all elliptic curves defined over Q by the celebrated effort of Wiles and his former students. In this lecture, I will consider the three-dimensional analogue of elliptic cuvres, namely, Calabi-Yau threefolds defined over Q. There is a special class of Calabi-Yau threefolds, rigid Calabi-Yau threefolds. I will formulate the modularity conjecture for rigid Calabi-Yau threefolds over Q. Then I will give evidence for its validity by a couple of examples. Also I will describe a strategy how one might attack the conjecture in the general setting.

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