{"id":12692,"date":"2001-12-09T00:00:00","date_gmt":"2001-12-09T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/on-the-tamagawa-number-conjecture\/"},"modified":"2001-12-09T00:00:00","modified_gmt":"2001-12-09T00:00:00","slug":"on-the-tamagawa-number-conjecture","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/on-the-tamagawa-number-conjecture\/","title":{"rendered":"On the tamagawa number conjecture"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Francesc Bars Cortina <\/strong><\/h2>\n<p>En la tesis se resuelve la conjetura del n\u00famero de tamagawa en dos situaciones: para curvas el\u00edpticas e+definidas sobre los racionales con multiplicaci\u00f3n compleja dada por el anillo de enteros de un cuerpo imaginario cuadr\u00e1tico k, y para caracteres de hecke que aplican adeles de k a k*.  en el caso de curvas el\u00edpticas, resolvemos la conjetura para los motivos h 1(e+)(k+2) con k entero mayor o igual a cero. El caso k=0 fue resuelto por bloch y kato (1990). Partiendo del resultado de kings sobre la conjetura para los motivos h 1(e+ x-(q)k) (k+2), hacemos el teorema del descenso. usamos t\u00e9cnicas de descenso galoisiano y probamos que el regulador de soul\u00e9 tiene descenso. Este estudio da el significado aritm\u00e9tico que daba la conjetura de tamagawa para el primer coeficiente no nulo del desenvolupamento de fourier de l(e+,s) en s=m para todo entero m diferente de 1.  para caracteres de hecke, estudiamos los motivos que vienen de hacer w-veces el producto tensorial del motivo h 1(e) aplic\u00e1ndole un idenpotente e (\/theta) y un twist de (w+k+1), donde w es un entero mayor que 0 y k mayor o igual que cero. E significa aqu\u00ed una curva el\u00edptica con multiplicaci\u00f3n compleja por k y definida sobre k, y el idempotente satisface que el numero elementos de \/theta es dos.  las funciones l asociadas vienen dadas por l(\/psi w,s) dondeo\/psi es el cm car\u00e1ceter asociado a e.  nuestro estudio utiliza el plilogaritmo el\u00edptico para comparar la conjetura de tamagawa en nuestra situaci\u00f3n con la conjetura principal de la teor\u00eda de iwasawa provada pro rubin. Nuestro estudio verifica el significado aritm\u00e9tico par al(\/psi w, k + w+1) dado por la conjetura.  tambi\u00e9n se resuelve la conjetura de jannsen, sobre la nulidad de un segundo grupo de cohomolog\u00eda de galois, para primos regulares en el caso de motivos de hecke anteriores. En la tesis se  compara el estudio global de la funci\u00f3n l para motivos de hecke con el estudio local, realizado por geisser,<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>On the tamagawa number conjecture<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 On the tamagawa number conjecture <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Francesc Bars Cortina <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 12\/09\/2001<\/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> Xarles Ribas Francesc Xavier<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: pilar Bayer isant <\/li>\n<li>Jos\u00e9 ignacio Burgos gil (vocal)<\/li>\n<li>adolfo Quiros gracian (vocal)<\/li>\n<li>j\u00ed\u00b6rg Wildeshaus (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Francesc Bars Cortina En la tesis se resuelve la conjetura del n\u00famero de tamagawa en dos situaciones: [&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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