DC Field | Value | Language |
---|---|---|
dc.contributor.author | Im, Bo-Hae | ko |
dc.date.accessioned | 2016-09-08T00:53:19Z | - |
dc.date.available | 2016-09-08T00:53:19Z | - |
dc.date.created | 2016-09-07 | - |
dc.date.created | 2016-09-07 | - |
dc.date.issued | 2007 | - |
dc.identifier.citation | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.359, no.12, pp.6143 - 6154 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | http://hdl.handle.net/10203/212950 | - |
dc.description.abstract | Let E/Q be an elliptic curve defined over Q of conductor N and let Gal((Q) over bar /Q) be the absolute Galois group of an algebraic closure Q of Q. For an automorphism sigma epsilon. Gal((Q) over bar /Q), we let (Q) over bar sigma s be the fixed sub field of Q under s. We prove that for every s. Gal((Q) over bar /Q), the Mordell-Weil group of E over the maximal Galois extension of Q contained in (Q) over bar sigma has in finite rank, so the rank of E((Q) over bar sigma) is in finite. Our approach uses the modularity of E/Q and a collection of algebraic points on E - the so-called Heegner points - arising from the theory of complex multiplication. In particular, we show that for some integer r and for a prime p prime to rN, the rank of E over all the ring class fields of a conductor of the form rp(n) is unbounded, as n goes to infinity | - |
dc.language | English | - |
dc.publisher | AMER MATHEMATICAL SOC | - |
dc.subject | RANK | - |
dc.title | Heegner points and Mordell-Weil groups of elliptic curves over large fields | - |
dc.type | Article | - |
dc.identifier.wosid | 000249224900019 | - |
dc.identifier.scopusid | 2-s2.0-54349108757 | - |
dc.type.rims | ART | - |
dc.citation.volume | 359 | - |
dc.citation.issue | 12 | - |
dc.citation.beginningpage | 6143 | - |
dc.citation.endingpage | 6154 | - |
dc.citation.publicationname | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.identifier.doi | 10.1090/S0002-9947-07-04364-4 | - |
dc.contributor.localauthor | Im, Bo-Hae | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | RANK | - |
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