{"id":78873,"date":"2018-03-09T23:24:35","date_gmt":"2018-03-09T23:24:35","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/la-jacobiana-de-un-cociente-hiperela%c2%adptico-de-la-curva-de-fermat-y-la-ley-de-reciprocidad-para-las-potencias-septimas\/"},"modified":"2018-03-09T23:24:35","modified_gmt":"2018-03-09T23:24:35","slug":"la-jacobiana-de-un-cociente-hiperela%c2%adptico-de-la-curva-de-fermat-y-la-ley-de-reciprocidad-para-las-potencias-septimas","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/geometria-algebraica\/la-jacobiana-de-un-cociente-hiperela%c2%adptico-de-la-curva-de-fermat-y-la-ley-de-reciprocidad-para-las-potencias-septimas\/","title":{"rendered":"La jacobiana de un cociente hiperel\u00edptico de la curva de fermat y la ley de reciprocidad para las potencias s\u00e9ptimas"},"content":{"rendered":"<h2>Tesis doctoral de <strong>  Echarri Hern\u00e1ndez Jos\u00e9 Miguel <\/strong><\/h2>\n<p>El objeto de esta tesis es dar una demostraci\u00f3n de la ley de reciprocidad para el s\u00edmbolo de las potencias s\u00e9ptimas, utilizando la aritm\u00e9tica de la curva y2 = x7 + 1\/4, que es una curva hiperel\u00edptica de g\u00e9nero tres.  su inspiraci\u00f3n principal ha sido un art\u00edculo de d.Grant en el que se prueba la ley de reciprocidad para el s\u00edmbolo de las potencias quintas a partir de la aritm\u00e9tica de la curva y2 = x5 + 1\/4, que es una curva hiperel\u00edptica de g\u00e9nero dos. respondiendo a una cuesti\u00f3n planteada expl\u00edcitamente en este art\u00edculo nosotros mostramos c\u00f3mo se deduce la ley de reciprocidad para el s\u00edmbolo de las potencias s\u00e9ptimas a partir de la aritm\u00e9tica de una curva que es imagen racional de la curva de fermat para p=7. las principales t\u00e9cnicas utilizadas son el estudio del grupo formal en el origen de la jacobiana y los teoremas de la multiplicaci\u00f3n compleja. Adem\u00e1s, para probar las leyes complementarias construimos unidades an\u00e1logas a las cl\u00e1sicas unidades el\u00edpticas evaluando funciones racionales en puntos de torsi\u00f3n.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>La jacobiana de un cociente hiperel\u00edptico de la curva de fermat y la ley de reciprocidad para las potencias s\u00e9ptimas<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 La jacobiana de un cociente hiperel\u00edptico de la curva de fermat y la ley de reciprocidad para las potencias s\u00e9ptimas <\/li>\n<li><strong>Autor:<\/strong>\u00a0  Echarri Hern\u00e1ndez Jos\u00e9 Miguel <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Pa\u00eds vasco\/euskal herriko unibertsitatea<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 27\/02\/2006<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Rosario Clement Fern\u00e1ndez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: pilar Bayer isant <\/li>\n<li>franciso Tahine parda (vocal)<\/li>\n<li>philippe Cassou-nogues (vocal)<\/li>\n<li>joan carles Lario loyo (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Echarri Hern\u00e1ndez Jos\u00e9 Miguel El objeto de esta tesis es dar una demostraci\u00f3n de la ley de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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