We show that for the primes l = 2, 3, 5, 7 or 13, there do not exist any non-zero abelian varieties over Q that have good reduction at every prime different from 1 and are semi-stable at l. We show that any semi-stable abelian variety over Q with good reduction outside l = 11 is isogenous to a power of the Jacobian variety of the modular curve X-0(11). In addition, we show that for l = 2,3 and 5, there do not exist any non-zero abelian varieties over Q with good reduction outside l that acquire semi-stable reduction at l over a tamely ramified extension.

Schoof, R. (2005). Abelian varieties over Q with bad reduction in one prime only. COMPOSITIO MATHEMATICA, 141(4), 847-868 [10.1112/S0010437X05001107].

Abelian varieties over Q with bad reduction in one prime only

SCHOOF, RENATUS JOHANNES
2005

Abstract

We show that for the primes l = 2, 3, 5, 7 or 13, there do not exist any non-zero abelian varieties over Q that have good reduction at every prime different from 1 and are semi-stable at l. We show that any semi-stable abelian variety over Q with good reduction outside l = 11 is isogenous to a power of the Jacobian variety of the modular curve X-0(11). In addition, we show that for l = 2,3 and 5, there do not exist any non-zero abelian varieties over Q with good reduction outside l that acquire semi-stable reduction at l over a tamely ramified extension.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - Geometria
English
Abelian varieties; Group schemes; Number fields; Semi-stable reduction
Schoof, R. (2005). Abelian varieties over Q with bad reduction in one prime only. COMPOSITIO MATHEMATICA, 141(4), 847-868 [10.1112/S0010437X05001107].
Schoof, Rj
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/37106
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