A Modular Non-Rigid Calabi-Yau Threefold
代数几何
2007-05-23 v2 数论
摘要
We construct an algebraic variety by resolving singularities of a quintic Calabi-Yau threefold. The middle cohomology of the threefold is shown to contain a piece coming from a pair of elliptic surfaces. The resulting quotient is a two-dimensional Galois representation. By using the Lefschetz fixed-point theorem in \'etale cohomology and counting points on the variety over finite fields, this Galois representation is shown to be modular.
引用
@article{arxiv.math/0508127,
title = {A Modular Non-Rigid Calabi-Yau Threefold},
author = {Edward Lee},
journal= {arXiv preprint arXiv:math/0508127},
year = {2007}
}
备注
34 pages; To appear in "Mirror Symmetry V", Proceedings of the BIRS Workshop on Calabi-Yau Varieties and Mirror Symmetry, December 6-11, 2003. Some typos in tables corrected, proof of Lemma 5.6 corrected