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ON ATKIN–LEHNER QUOTIENTS OF SHIMURA CURVES
Published online by Cambridge University Press: 01 November 1999
Abstract
We study the Čerednik–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.
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- © The London Mathematical Society 1999
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