If A/K is an abelian variety over a number field and P and Q are rational points, the original support conjecture asserted that if the order of Q (mod p) divides the order of P (mod P) for almost all primes p of K, then Q is obtained from P by applying an endomorphism of A. This is now known to be untrue. In this note we prove that it is not even true modulo the torsion of A. (c) 2005 Elsevier Inc. All rights reserved.

Larsen, M., & Schoof, R. (2006). A refined counter-example to the support conjecture for abelian varieties. JOURNAL OF NUMBER THEORY, 116(2), 396-398 [10.1016/j.jnt.2005.05.015].

A refined counter-example to the support conjecture for abelian varieties

SCHOOF, RENATUS JOHANNES
2006

Abstract

If A/K is an abelian variety over a number field and P and Q are rational points, the original support conjecture asserted that if the order of Q (mod p) divides the order of P (mod P) for almost all primes p of K, then Q is obtained from P by applying an endomorphism of A. This is now known to be untrue. In this note we prove that it is not even true modulo the torsion of A. (c) 2005 Elsevier Inc. All rights reserved.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - Geometria
eng
Larsen, M., & Schoof, R. (2006). A refined counter-example to the support conjecture for abelian varieties. JOURNAL OF NUMBER THEORY, 116(2), 396-398 [10.1016/j.jnt.2005.05.015].
Larsen, M; Schoof, R
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/38845
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact