Good reduction of abelian varieties
نویسندگان
چکیده
منابع مشابه
Semi-stable abelian varieties with good reduction outside 15
We show that there are no non-zero semi-stable abelian varieties over Q( √ 5) with good reduction outside 3 and we show that the only semi-stable abelian varieties over Q with good reduction outside 15 are, up to isogeny over Q, powers of the Jacobian of the modular curve X0(15).
متن کاملII Università degli Studi di Roma Semistable abelian varieties with good reduction outside 15 . René
We show that there are no non-zero semi-stable abelian varieties over Q( √ 5) with good reduction outside 3 and we show that the only semi-stable abelian varieties over Q with good reduction outside 15 are, up to isogeny over Q, powers of the Jacobian of the modular curve X0(15).
متن کاملII Università degli Studi di Roma Semistable abelian varieties with good reduction outside 15
We show that there are no non-zero semi-stable abelian varieties over Q( √ 5) with good reduction outside 3 and we show that the only semi-stable abelian varieties over Q with good reduction outside 15 are, up to isogeny over Q, powers of the Jacobian of the modular curve X0(15).
متن کاملAbelian varieties over cyclotomic fields with good reduction everywhere
For every conductor f ∈ {1, 3, 4, 5, 7, 8, 9, 11, 12, 15} there exist non-zero abelian varieties over the cyclotomic field Q(ζf ) with good reduction everywhere. Suitable isogeny factors of the Jacobian variety of the modular curve X1(f ) are examples of such abelian varieties. In the other direction we show that for all f in the above set there do not exist any non-zero abelian varieties over ...
متن کاملStudi di Roma Abelian varieties over Q with bad reduction in one prime only
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 l 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 X0(11). In addition we show that for l = 2, 3 and 5...
متن کاملdegli Studi di Roma Semi - stable abelian varieties over Q with bad reduc - tion in one prime only
Let l be a prime. We show that there do not exist any non-zero semi-stable abelian varieties over Q with good reduction outside l if and only if l = 2, 3, 5, 7 or 13. 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 X0(11). In addition we show that there do not exist any non-zero abelian v...
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