Root numbers and parity of ranks of elliptic curves
Identifieur interne : 000B17 ( Istex/Corpus ); précédent : 000B16; suivant : 000B18Root numbers and parity of ranks of elliptic curves
Auteurs : Tim Dokchitser ; Vladimir DokchitserSource :
- Journal für die reine und angewandte Mathematik (Crelles Journal) [ 0075-4102 ] ; 2011-09.
English descriptors
- KwdEn :
- Abelian, Burnside ring, Conjecture, Continuity argument, Corollary, Dokchitser, Eld, Elliptic, Elliptic curve, Elliptic curves, Galois, Galois extension, Galois group, Global root number, Good reduction, Hilbert, Hilbert symbol, Isogeny, Local root numbers, Local terms, Multiplicative, Multiplicative reduction, Nite, Ord2, Ord3, Ordp, Other hand, Other words, Parity, Parity conjecture, Product formula, Quadratic, Quadratic extension, Quadratic twist, Quadratic twists, Real number, Root number, Root numbers, Same parity, Selmer, Selmer group, Selmer groups, Selmer rank, Semistable, Theorem theorem, Vladimir, Vladimir dokchitser.
- Teeft :
- Abelian, Burnside ring, Conjecture, Continuity argument, Corollary, Dokchitser, Eld, Elliptic, Elliptic curve, Elliptic curves, Galois, Galois extension, Galois group, Global root number, Good reduction, Hilbert, Hilbert symbol, Isogeny, Local root numbers, Local terms, Multiplicative, Multiplicative reduction, Nite, Ord2, Ord3, Ordp, Other hand, Other words, Parity, Parity conjecture, Product formula, Quadratic, Quadratic extension, Quadratic twist, Quadratic twists, Real number, Root number, Root numbers, Same parity, Selmer, Selmer group, Selmer groups, Selmer rank, Semistable, Theorem theorem, Vladimir, Vladimir dokchitser.
Abstract
The purpose of the paper is to complete several global and local results concerning parity of ranks of elliptic curves. Primarily, we show that the Shafarevich–Tate conjecture implies the parity conjecture for all elliptic curves over number fields, we give a formula for local and global root numbers of elliptic curves and complete the proof of a conjecture of Kramer and Tunnell in characteristic 0. The method is to settle the outstanding local formulae by deforming from local fields to totally real number fields and then using global parity results.
Url:
DOI: 10.1515/crelle.2011.060
Links to Exploration step
ISTEX:35B3B0263FD154132798BAC3C6D3AEFF4F97F640Le document en format XML
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November 2009.</string-date></date><date date-type="rev-recd"><day>25</day><month>04</month><year>2010</year><string-date>in revidierter Fassung 25. April 2010.</string-date></date></history><copyright-statement>© Walter de Gruyter Berlin · New York 2011</copyright-statement><copyright-year>2011</copyright-year><related-article related-article-type="pdf" xlink:href="crelle.2011.060.pdf"></related-article><abstract><title>Abstract</title><p>The purpose of the paper is to complete several global and local results concerning parity of ranks of elliptic curves. Primarily, we show that the Shafarevich–Tate conjecture implies the parity conjecture for all elliptic curves over number fields, we give a formula for local and global root numbers of elliptic curves and complete the proof of a conjecture of Kramer and Tunnell in characteristic 0. The method is to settle the outstanding local formulae by deforming from local fields to totally real number fields and then using global parity results.</p></abstract></article-meta></front></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Root numbers and parity of ranks of elliptic curves</title></titleInfo><titleInfo type="alternative" lang="en" contentType="CDATA"><title>Root numbers and parity of ranks of elliptic curves</title></titleInfo><name type="personal"><namePart type="given">Tim</namePart><namePart type="family">Dokchitser</namePart><affiliation>Robinson College, Cambridge CB3 9AN, United Kingdom</affiliation><affiliation>Robinson College, Cambridge CB3 9AN, United Kingdom</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Vladimir</namePart><namePart type="family">Dokchitser</namePart><affiliation>Emmanuel College, Cambridge CB2 3AP, United Kingdom</affiliation><affiliation>Emmanuel College, Cambridge CB2 3AP, United Kingdom</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Walter de Gruyter GmbH & Co. KG</publisher><dateIssued encoding="w3cdtf">2011-09</dateIssued><dateCreated encoding="w3cdtf">2011-03-23</dateCreated><copyrightDate encoding="w3cdtf">2011</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><abstract lang="en">The purpose of the paper is to complete several global and local results concerning parity of ranks of elliptic curves. Primarily, we show that the Shafarevich–Tate conjecture implies the parity conjecture for all elliptic curves over number fields, we give a formula for local and global root numbers of elliptic curves and complete the proof of a conjecture of Kramer and Tunnell in characteristic 0. The method is to settle the outstanding local formulae by deforming from local fields to totally real number fields and then using global parity results.</abstract><relatedItem type="host"><titleInfo><title>Journal für die reine und angewandte Mathematik (Crelles Journal)</title></titleInfo><titleInfo type="abbreviated"><title>Journal für die reine und angewandte Mathematik (Crelles Journal)</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><originInfo></originInfo><identifier type="ISSN">0075-4102</identifier><identifier type="eISSN">1435-5345</identifier><identifier type="PublisherID">crll</identifier><part><date>2011</date><detail type="volume"><caption>vol.</caption><number>2011</number></detail><detail type="issue"><caption>no.</caption><number>658</number></detail><extent unit="pages"><start>39</start><end>64</end></extent></part></relatedItem><identifier type="istex">35B3B0263FD154132798BAC3C6D3AEFF4F97F640</identifier><identifier type="ark">ark:/67375/QT4-NH0T0T51-Q</identifier><identifier type="DOI">10.1515/crelle.2011.060</identifier><identifier type="ArticleID">crll.2011.658.39</identifier><identifier type="pdf">crelle.2011.060.pdf</identifier><accessCondition type="use and reproduction" contentType="copyright">© Walter de Gruyter Berlin · New York 2011, 2011</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-B4QPMMZB-D">degruyter-journals</recordContentSource><recordOrigin>© Walter de Gruyter Berlin · New York 2011</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/35B3B0263FD154132798BAC3C6D3AEFF4F97F640/metadata/json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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