2022/09/07 by Philippe Michaud‐Jacobs, Michaud-Jacobs, Philippe
Mathematics · #Algebraic Geometry and Number Theory #History and Theory of Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2209.03153
Mazur's isogeny theorem states that if p is a prime for which there exists an elliptic curve E / ℚ that admits a rational isogeny of degree p, then p ∈ \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.