{"id":36842,"date":"1998-01-01T00:00:00","date_gmt":"1998-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/on-motives-and-moduli-spaces-of-stable-vector-bundles-over-a-curve\/"},"modified":"1998-01-01T00:00:00","modified_gmt":"1998-01-01T00:00:00","slug":"on-motives-and-moduli-spaces-of-stable-vector-bundles-over-a-curve","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/on-motives-and-moduli-spaces-of-stable-vector-bundles-over-a-curve\/","title":{"rendered":"On motives and moduli spaces of stable vector bundles over a curve."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jos\u00e9 Sebastian Del Ba\u00f1o Rollin <\/strong><\/h2>\n<p>Se ha realizado un estudio mot\u00edvico de los espacios de moduli de fibrados semiestables sobre una curva algebraica, desarrollando a su vez las t\u00e9cnicas necesarias en teor\u00eda de motivos.  en teor\u00eda de motivos.  g-motivos: consideramos motivos para esquemas con una acci\u00f3n por un grupo finito. definimos functores de inducci\u00f3n y restricci\u00f3n para esquemas y motivos y demostramos un teorema que garantiza la conmutaci\u00f3n de dos factores. Un corolario de este teorema es una conjetura de denef y loeser en.  potencias sim\u00e9tricas: damos una expresi\u00f3n para el motivo de la potencia sim\u00e9trica de una variedad proyectiva y lisa. Ello es consecuencia de un formalismo categ\u00f3rico que llamamos lambda estructura.  localizaci\u00f3n: si un toro algebraico opera sobre una variedad lisa y proyectiva obtenemos una expresi\u00f3n para el motivo de chow, grupos de chow y k-teor\u00eda de la variedad inicial en funci\u00f3n de las variedades de puntos fijos.  motivos de los espacios de moduli.  rango dos: encontramos una expresi\u00f3n para el polinomio de poincar\u00e9 mot\u00edvico del espacio de moduli de fibrados de rango dos y determianante de grado uno fijado. De esta f\u00f3rmula puede obtenerse los n\u00fameros de hodge del espacio de moduli as\u00ed como una f\u00f3rmula para el n\u00famero de puntos sobre un cuerpo finito obtenida por harder usando m\u00e9todos ad\u00e9lico. En el caso de determinante trivial, encontramos f\u00f3rmulas an\u00e1logas para el modelo liso de seshadri del espacio de moduli se la caracter\u00edstica del cuerpo base es nula. Probamos que la estructura de hodge mixta del espacio de moduli singular s\u00f3lo tiene dos pesos.  rango arbitrario: damos un versi\u00f3n mot\u00edvica de la f\u00f3rmula de recursi\u00f3n de atiyah-bott e inverimos esta rtecursi\u00f3n usando el m\u00e9todo de laumon-rapoport. Probamos que el motivo del espacio de moduli est\u00e1 en la categor\u00eda generada por el motivo de la curva.  en ambos casos encontramos conexiones entre ciertas conjeturas para los espacios de<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>On motives and moduli spaces of stable vector bundles over a curve.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 On motives and moduli spaces of stable vector bundles over a curve. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jos\u00e9 Sebastian Del Ba\u00f1o Rollin <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de catalunya<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1998<\/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>Pere Pascual Gainza<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: sebasti\u00e1n Xamb\u00f3 descamps <\/li>\n<li>ezra Getzler (vocal)<\/li>\n<li>m.s. Narasimham (vocal)<\/li>\n<li>Francisco Guill\u00e9n santos (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jos\u00e9 Sebastian Del Ba\u00f1o Rollin Se ha realizado un estudio mot\u00edvico de los espacios de moduli 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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[583,126,15596],"tags":[97229,97231,97228,97230,38937,9616],"class_list":["post-36842","post","type-post","status-publish","format-standard","hentry","category-geometria","category-matematicas","category-politecnica-de-catalunya","tag-ezra-getzler","tag-francisco-guillen-santos","tag-jose-sebastian-del-bano-rollin","tag-m-s-narasimham","tag-pere-pascual-gainza","tag-sebastian-xambo-descamps"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/36842","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=36842"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/36842\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=36842"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=36842"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=36842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}