Modularity of rigid Calabi-Yau threefolds over Q
Luis Dieulefait, Jayanta Manoharmayum
TL;DR
This paper proves the modularity of a large class of rigid Calabi-Yau threefolds over the rationals, specifically those with good reduction at 3 and 7, advancing understanding of their arithmetic properties.
Contribution
It establishes the modularity of rigid Calabi-Yau threefolds over Q with good reduction at 3 and 7, a significant extension in the field of algebraic geometry and number theory.
Findings
Proves modularity for rigid Calabi-Yau threefolds with good reduction at 3 and 7
Extends the class of known modular Calabi-Yau threefolds over Q
Provides new insights into the arithmetic of Calabi-Yau threefolds
Abstract
We prove modularity for a huge class of rigid Calabi-Yau threefolds over . In particular we prove that every rigid Calabi-Yau threefold with good reduction at 3 and 7 is modular.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometric and Algebraic Topology