On Atkin-Lehner Quotients of Curves
From MaRDI portal
Publication:4487629
DOI10.1112/S0024609399006335zbMATH Open1024.11043arXivmath/9802136MaRDI QIDQ4487629
Author name not available (Why is that?)
Publication date: 22 June 2000
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/math/9802136
No records found.
No records found.
This page was built for publication: On Atkin-Lehner Quotients of Curves
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4487629)
