Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Manin-Mumford conjecture for abelian varieties with a prime of supersingular reduction


Author: Tetsushi Ito
Journal: Proc. Amer. Math. Soc. 134 (2006), 2857-2860
MSC (2000): Primary 14K12; Secondary 11G10, 14G15
Published electronically: May 1, 2006
MathSciNet review: 2231608
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a short proof of the `` prime-to-$ p$ version" of the Manin-Mumford conjecture for an abelian variety over a number field, when it has supersingular reduction at a prime dividing $ p$, by combining the methods of Bogomolov, Hrushovski, and Pink-Roessler. Our proof here is quite simple and short, and neither $ p$-adic Hodge theory nor model theory is used. The observation is that a power of a lift of the Frobenius element at a supersingular prime acts on the prime-to-$ p$ torsion points via nontrivial homothety.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14K12, 11G10, 14G15

Retrieve articles in all journals with MSC (2000): 14K12, 11G10, 14G15


Additional Information

Tetsushi Ito
Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan
Email: tetsushi@math.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08518-2
PII: S 0002-9939(06)08518-2
Received by editor(s): December 7, 2004
Received by editor(s) in revised form: April 28, 2005
Published electronically: May 1, 2006
Communicated by: Michael Stillman
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.