On Atkin-Lehner quotients of Shimura curves

Details On Atkin-Lehner quotients of Shimura curves On Atkin-Lehner quotients of Shimura curves

1998-02-06

arxiv.org/abs/math/9802136v1

Mathematics

Number Theory

Scientific paper

Poonen and Stoll have shown that the reduced Shafarevich-Tate group of a principally polarized abelian variety over a global field can have order twice a square (the odd case) as well as a square (the even case). For a curve over a global field, they give a local diophantine criterion for its jacobian to be even or odd. In this note we use the Cherednik-Drinfeld p-adic uniformization to study the local points and divisors on certain Atkin-Lehner quotients of Shimura curves. We exhibit an explicit family of such quotient curves over the rationals with odd jacobians, with genus going to infinity, and with at most finitely many hyperelliptic members.

Affiliated with

Also associated with

No associations

Rating

On Atkin-Lehner quotients of Shimura curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Atkin-Lehner quotients of Shimura curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Atkin-Lehner quotients of Shimura curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-423880