On <i>p</i>-adic uniformization of abelian varieties with good reduction

Good reduction of abelian varieties

P -adic Uniformization of Unitary Shimura Varieties

Introduction Let Γ ⊂ PGUd−1,1(R) 0 be a torsion-free cocompact lattice. Then Γ acts on the unit ball B ⊂ C by holomorphic automorphisms. The quotient Γ\B is a complex manifold, which has a unique structure of a complex projective variety XΓ (see [Sha, Ch. IX, §3]). Shimura had proved that when Γ is an arithmetic congruence subgroup, XΓ has a canonical structure of a projective variety over some...

Abelian 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 ...

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).

Local Heights on Abelian Varieties and Rigid Analytic Uniformization

We express classical and p-adic local height pairings on an abelian variety with split semistable reduction in terms of the corresponding pairings on the abelian part of the Raynaud extension (which has good reduction). Here we use an approach to height pairings via splittings of biextensions which is due to Mazur and Tate. We conclude with a formula comparing Schneider's p-adic height pairing ...