{"title":"泛变形族中的p进l函数","authors":"David Loeffler","doi":"10.1007/s40316-021-00187-1","DOIUrl":null,"url":null,"abstract":"<div><p>We construct examples of <i>p</i>-adic <i>L</i>-functions over universal deformation spaces for <span>\\({{\\,\\mathrm{GL}\\,}}_2\\)</span>. We formulate a conjecture predicting that the natural parameter spaces for <i>p</i>-adic <i>L</i>-functions and Euler systems are not the usual eigenvarieties (parametrising nearly-ordinary families of automorphic representations), but other, larger spaces depending on a choice of a parabolic subgroup, which we call ‘big parabolic eigenvarieties’.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","pages":"117 - 137"},"PeriodicalIF":0.5000,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-021-00187-1.pdf","citationCount":"7","resultStr":"{\"title\":\"P-adic L-functions in universal deformation families\",\"authors\":\"David Loeffler\",\"doi\":\"10.1007/s40316-021-00187-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We construct examples of <i>p</i>-adic <i>L</i>-functions over universal deformation spaces for <span>\\\\({{\\\\,\\\\mathrm{GL}\\\\,}}_2\\\\)</span>. We formulate a conjecture predicting that the natural parameter spaces for <i>p</i>-adic <i>L</i>-functions and Euler systems are not the usual eigenvarieties (parametrising nearly-ordinary families of automorphic representations), but other, larger spaces depending on a choice of a parabolic subgroup, which we call ‘big parabolic eigenvarieties’.</p></div>\",\"PeriodicalId\":42753,\"journal\":{\"name\":\"Annales Mathematiques du Quebec\",\"volume\":\"47 1\",\"pages\":\"117 - 137\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40316-021-00187-1.pdf\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Mathematiques du Quebec\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40316-021-00187-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematiques du Quebec","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40316-021-00187-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
P-adic L-functions in universal deformation families
We construct examples of p-adic L-functions over universal deformation spaces for \({{\,\mathrm{GL}\,}}_2\). We formulate a conjecture predicting that the natural parameter spaces for p-adic L-functions and Euler systems are not the usual eigenvarieties (parametrising nearly-ordinary families of automorphic representations), but other, larger spaces depending on a choice of a parabolic subgroup, which we call ‘big parabolic eigenvarieties’.
期刊介绍：
The goal of the Annales mathématiques du Québec (formerly: Annales des sciences mathématiques du Québec) is to be a high level journal publishing articles in all areas of pure mathematics, and sometimes in related fields such as applied mathematics, mathematical physics and computer science.
Papers written in French or English may be submitted to one of the editors, and each published paper will appear with a short abstract in both languages.
History:
The journal was founded in 1977 as „Annales des sciences mathématiques du Québec”, in 2013 it became a Springer journal under the name of “Annales mathématiques du Québec”. From 1977 to 2018, the editors-in-chief have respectively been S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea.
Les Annales mathématiques du Québec (anciennement, les Annales des sciences mathématiques du Québec) se veulent un journal de haut calibre publiant des travaux dans toutes les sphères des mathématiques pures, et parfois dans des domaines connexes tels les mathématiques appliquées, la physique mathématique et l''informatique.
On peut soumettre ses articles en français ou en anglais à l''éditeur de son choix, et les articles acceptés seront publiés avec un résumé court dans les deux langues.
Histoire:
La revue québécoise “Annales des sciences mathématiques du Québec” était fondée en 1977 et est devenue en 2013 une revue de Springer sous le nom Annales mathématiques du Québec. De 1977 à 2018, les éditeurs en chef ont respectivement été S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea.
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