The Shimura-Taniyama Conjecture and Conformal Field Theory
高能物理 - 理论
2014-11-18 v1 代数几何
摘要
The Shimura-Taniyama conjecture states that the Mellin transform of the Hasse-Weil L-function of any elliptic curve defined over the rational numbers is a modular form. Recent work of Wiles, Taylor-Wiles and Breuil-Conrad-Diamond-Taylor has provided a proof of this longstanding conjecture. Elliptic curves provide the simplest framework for a class of Calabi-Yau manifolds which have been conjectured to be exactly solvable. It is shown that the Hasse-Weil modular form determined by the arithmetic structure of the Fermat type elliptic curve is related in a natural way to a modular form arising from the character of a conformal field theory derived from an affine Kac-Moody algebra.
引用
@article{arxiv.hep-th/0211284,
title = {The Shimura-Taniyama Conjecture and Conformal Field Theory},
author = {Rolf Schimmrigk and Sean Underwood},
journal= {arXiv preprint arXiv:hep-th/0211284},
year = {2014}
}