WebJacobian varieties J0(l2) of the modular curves X0(l2) are other examples of abelian vari- eties over Q that have good reduction at all primes different from l. These abelian varieties are not semi-stable at l. However, S.J. Edixhoven [5] showed that J0(l2) acquires semi- stable reduction at l over an extension that is merely tamely ramified at l. WebThe Hecke orbit conjecture asserts that every prime-to- Hecke orbit in a Shimura variety is dense in the central leaf containing it. In this paper, we prove the conjecture for certain …
Galois representations attached to Q-curves and the
Weban imaginary quadratic field K with a prime of bad reduction greater than 6 has a surjective mod p Galois representation. The bound on p depends on K and the degree of the isogeny ... one wonders whether modular abelian varieties can address the classical problem of describing all solutions to the generalized Fermat equation Ap +Bq = Cr (1.1) bj\u0027s in olean ny
Arithmetik und Geometrie algebraischer Zyklen: Verfahren des …
WebOur second result concerns abelian varieties over Q that have good reduction outside l and acquire semi-stable reduction at l over a tamely ramified extension. Theorem 1.3. For the primesl =2,3 or 5, there do not exist any non-zero abelian varieties over Q that have good reduction at every prime different from l and acquire semi-stable ... WebABELIAN VARIETIES WITH POTENTIALLY ORDINARY REDUCTION 817 is a P:= P(a) ∈ Q p.Thena is an analytic function of the rigid analytic space associatedtoSpf(I)(inthesenseofBerthelotasin[dJ],Section7). Each (reduced) irreducible component Spec(I) ⊂ Spec(h) has a 2-dimensional absolutely irreducible continuous … WebTorp(A)∩ X is Zariski dense in X,thenX is a translate of an abelian subvariety of A, that is, X = A +a,whereA is an abelian subvariety of A and a ∈ A. Proof. Let A F be the reduction of A at v, which is a supersingular abelian va-riety over F.Letq be the cardinality of F,whichisapowerofp.Letσ ∈ Gal(F/F)betheq-th power Frobenius ... dating sites for italian american