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.
| Original language | English |
|---|---|
| Pages (from-to) | 681-685 |
| Number of pages | 5 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 31 |
| Issue number | 6 |
| DOIs | |
| State | Published - Nov 1999 |