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ON ATKIN–LEHNER QUOTIENTS OF SHIMURA CURVES

Published online by Cambridge University Press:  01 November 1999

BRUCE W. JORDAN  and
RON LIVNÉ
BRUCE W. JORDAN
Affiliation:
Department of Mathematics, Baruch College, CUNY, 17 Lexington Avenue, New York, NY 10010, USA
RON LIVNÉ
Affiliation:
Mathematics Institute, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel
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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.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 6 , November 1999 , pp. 681 - 685
Copyright
© The London Mathematical Society 1999

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