论文标题
Mazur的等级定理
Mazur's isogeny theorem
论文作者
论文摘要
Mazur的同根定理指出，如果$ p $是椭圆曲线$ e / \ mathbb {q} $的主要水平，则承认合理的$ p $ $ p $的同学，然后是$ p \ in \ in \ in \ in \ {2,3,5,1113,13,13,17,17,17,17,19,19,19,37,437,437,437,437,437,16333 c。该结果是椭圆曲线理论的基石之一，在Fermat的最后定理证明中起着至关重要的作用。在这篇说明性论文中，我们概述了Mazur对该定理的证明，其中模块化曲线和GALOIS表示突出。
Mazur's isogeny theorem states that if $p$ is a prime for which there exists an elliptic curve $E / \mathbb{Q}$ that admits a rational isogeny of degree $p$, then $p \in \{2,3,5,7,11,13,17,19,37,43,67,163 \}$. This result is one of the cornerstones of the theory of elliptic curves and plays a crucial role in the proof of Fermat's Last Theorem. In this expository paper, we overview Mazur's proof of this theorem, in which modular curves and Galois representations feature prominently.
