Rigid Calabi-Yau Threefolds over Q Are Modular

Abstract

The proof of Serre's conjecture on Galois representations over finite fields allows us to show, using a method due to Serre himself, that all rigid Calabi-Yau threefolds defined over Q are modular.

Final version to appear in Expositiones Mathematicae

References in corpus (1)

• A modular quintic Calabi-Yau threefold of level 55

Cited by in corpus (4)

• Supersymmetric Flux Compactifications and Calabi-Yau Modularity
• Flux Modularity, F-Theory, and Rational Models
• New realizations of modular forms in Calabi-Yau threefolds arising from ${\varphi }^4$ theory
• On the Arithmetic of D-brane Superpotentials. Lines and Conics on the Mirror Quintic