Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma
Identifieur interne : 000466 ( Istex/Corpus ); précédent : 000465; suivant : 000467Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma
Auteurs : William SteinSource :
- Algorithms and Computation in Mathematics [ 1431-1550 ] ; 2006.
Abstract
Abstract : In this paper we describe the Birch and Swinnerton-Dyer conjecture in the case of modular abelian varieties and how to use Magma to do computations with some of the quantities that appear in the conjecture. We assume the reader has some experience with algebraic varieties and number theory, but do not assume the reader has proficiency working with elliptic curves, abelian varieties, modular forms, or modular symbols. The computations give evidence for the Birch and Swinnerton- Dyer conjecture and increase our explicit understanding of modular abelian varieties.
Url:
DOI: 10.1007/978-3-540-37634-7_4
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We assume the reader has some experience with algebraic varieties and number theory, but do not assume the reader has proficiency working with elliptic curves, abelian varieties, modular forms, or modular symbols. The computations give evidence for the Birch and Swinnerton- Dyer conjecture and increase our explicit understanding of modular abelian varieties.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma</title></titleInfo><name type="personal"><namePart type="given">William</namePart><namePart type="family">Stein</namePart><affiliation>Department of Mathematics, Harvard University, Cambridge, MA, USA</affiliation><affiliation>E-mail: was@math.harvard.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="research-article" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2006</dateIssued><dateIssued encoding="w3cdtf">2006</dateIssued><copyrightDate encoding="w3cdtf">2006</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract : In this paper we describe the Birch and Swinnerton-Dyer conjecture in the case of modular abelian varieties and how to use Magma to do computations with some of the quantities that appear in the conjecture. 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