On Atkin-lehner Quotients of Shimura Curves

  title={On Atkin-lehner Quotients of Shimura Curves},
  author={Bruce W M Jordan and RON LIVN{\'E}},
We study thě Cerednik-Drinfeld p-adic uniformization of certain Atkin-Lehner quotients of Shimura curves over Q. We use it to determine over which local fields they have rational points and divisors of a given degree. Using a criterion of Poonen and Stoll we show that the Shafarevich-Tate group of their jacobians is not of square order for infinitely many cases. In [PSt] Poonen and Stoll have shown that if the Shafarevich-Tate group of a principally polarized abelian variety A over a global… CONTINUE READING
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