Steinitz class of Mordell groups of elliptic curves with complex multiplication
| dc.creator | Liu, Tong | |
| dc.creator | Zhang, Xianke | |
| dc.date | 1998-09-03 | |
| dc.date.accessioned | 2026-07-07T05:26:15Z | |
| dc.date.available | 2026-07-07T05:26:15Z | |
| dc.description | Let E be an elliptic curve having Complex Multiplication by the full ring O_K of integers of K=Q(\sqrt{-D}), let H=K(j(E)) be the Hilbert class field of K. Then the Mordell-Weil group E(H) is an O_K-module, and its structure denpends on its Steinitz class St(E), which is studied here. In partucular, when D is a prime number, it is proved that St(E)=1 if D\equiv 3 (mod 4); and St(E)=[P]^t if D\equiv 1 (mod 4), where [P] is the ideal class of K represented by prime factor P of 2 in K, t is a fixed integer. General structures are also discussed for St(E) and for modules over Dedekind domain. These results develop the results by D. Dummit and W. Miller for D=10 and some elliptic curves to more general D and general elliptic curves. | |
| dc.identifier | https://arxiv.org/abs/math/9809208 | |
| dc.identifier | http://arxiv.org/abs/math/9809208 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77481 | |
| dc.subject | Number Theory | |
| dc.title | Steinitz class of Mordell groups of elliptic curves with complex multiplication | |
| dc.type | text |