World Library  
Flag as Inappropriate
Email this Article

Mazur's torsion theorem

Article Id: WHEBN0001082618
Reproduction Date:

Title: Mazur's torsion theorem  
Author: World Heritage Encyclopedia
Language: English
Subject: Faltings' theorem, List of theorems, Modular curve, Beppo Levi, Barry Mazur
Publisher: World Heritage Encyclopedia

Mazur's torsion theorem

In algebraic geometry Mazur's torsion theorem, due to Barry Mazur, classifies the possible torsion subgroups of the group of rational points on an elliptic curve defined over the rational numbers.

If Cn denotes the cyclic group of order n, then the possible torsion subgroups are Cn with 1 ≤ n ≤ 10, and also C12; and the direct sum of C2 with C2, C4, C6 or C8.

In the opposite direction, all these torsion structures occur infinitely often over Q since the corresponding modular curves are of genus zero.


  • Mazur, Barry: Rational isogenies of prime degree, Inventiones Math. 44, 2 (June 1978), pp 129–162.

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.