The modularity/automorphy of Calabi-Yau varieties of CM type

Yui, Noriko

doi:10.1090/pspum/096/01659

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Conference Paper

The modularity/automorphy of Calabi-Yau varieties of CM type

MPS-Authors

/persons/resource/persons236494

Yui, Noriko
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1090/pspum/096
(Publisher version)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

Yui, N. (2017). The modularity/automorphy of Calabi-Yau varieties of CM type. In String-Math 2015: December 31, 2015-January 4, 2016, Tsinghua Sanya International Mathematics Forum, Sanya, China (pp. 265-297). Providence, RI: American Mathematical Society.

Cite as: https://hdl.handle.net/21.11116/0000-0004-6A0E-7

Abstract

We consider Calabi–Yau varieties of dimension
d ≤ 3 defined over Q, and address the modularity/automorphy of such Calabi–Yau varieties. When the dimension of the associated Galois representations are large, e.g., >2, the problem poses a serious challenge and is out of reach in the general situations.
In this paper, I will concentrate on Calabi–Yau varieties of CM type, and establish their (motivic) modularity/automorphy. The expositions are focused on two examples: K3 surfaces with non-symplectic automorphisms, and Calabi-Yau threefolds of Borcea–Voisin type. We will briefly discuss arithmetic mirror symmetry for quite specific examples of K3 surfaces and Calabi–Yau threefolds of Borcea–Voisin type.