On the modularity of rigid Calabi-Yau threefolds: epilogue (Q393222)

The modularity of rigid Calabi-Yau threefolds defined over \(\mathbb{Q}\) was established by \textit{F. Q. Gouvêa} and \textit{N. Yui} in [Expo. Math. 29, No. 1, 142--149 (2011; Zbl 1230.14056)]. Their proof rests on the Serre's conjecture (now a theorem) of the modularity of the residual two-dimensional Galois representations. This involves residual modularity in infinitely many characteristics. This article gives an alternative approach, namely, the author uses the residual modularity in a certain characteristic, and this is combined with the effective Chebotarev theorem.