{"title":"Metrised ample line bundles in non-Archimedean geometry","authors":"Yan-Long Fang","doi":"10.5802/aif.3549","DOIUrl":"https://doi.org/10.5802/aif.3549","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48135798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract : let k be a finite field of characteristic p>0, W(k) the ring of Witt vectors of k, X a smooth scheme over spec W(k) and X_0 the special fiber of X.In 1987, Deligne and Illusie proved the degeneration of the spectralsequence ``de Hodge vers de Rham'' in a purely algebraic way, by constructing aquasi-isomorphism at the level of derived categories between the de Rham complex of X_0 with a complex with 0 differentials. Simultaneously Fontaine and Messingconstructed a divided Frobenius map on the crystalline complexes associated with X_0. We show that bothmorphisms of derived categories are compatible mod p>0 if the dimension of X_0 is 0, W(k) l'anneau des vecteurs de Witt de k, X un schema lisse sur spec W(k), X_0 la fibre speciale de X. En 1987, Deligne et Illusie ont demontre la degenerescence de la suitespectrale de Hodge vers de Rham d'une facon purement algebrique, en construisantun quasi-isomorphisme dans la categorie derivee entre le complexe de de Rham de X_0 et un complexe a differentielles nulles. Concomitamment, Fontaine et Messing ont construit un Frobenius divise sur les complexes cristallinsassocies a X_0. Nous montrons que ces deux morphismes de categories derivees sont compatibles. Comme application de cette compatibilite, nous donnons la structure du phi-module filtre mod p associe a la courbe de Drinfeld.
文摘:让k的有限域特征p > 0, W (k) k的威特向量环,X平稳计划/规范 W (k)和X_0 X.In 1987的特殊纤维,Deligne的变性和Illusie spectralsequence“德·霍奇更de Rham”在一个纯粹代数方法,通过构造aquasi-isomorphism的派生类从德Rham复杂之间的差异与一个复杂的0。同时，Fontaine和messinge在与X_0相关的晶体配合物上构造了一个分裂的Frobenius图。我们表明bothmorphisms派生类别是兼容的mod p > 0如果X_0的维数为0,W (k) l 'anneau des为了德威特·德·k, X联合国模式lisse苏尔规范W (k),从拉纤维speciale de X En 1987 Deligne et Illusie位于安大略省demontre la degenerescence de la suitespectrale de霍奇更de Rham这样一个purement algebrique, En construisantun quasi-isomorphisme在categorie derivee之间le complexe de de Rham de X_0等联合国complexe differentielles null。承诺，Fontaine和Messing构建了Frobenius划分的复杂的晶体，在x0的结合部。Nous montrons que ces deux morphismes de categories派生出soncompatibles。Comme应用程序的数据兼容，现在的donons，结构的phili -模块过滤模型的关联，一个courbe de Drinfeld。
{"title":"Interprétation cristalline de l’isomorphisme de Deligne–Illusie","authors":"C. Huyghe, N. Wach","doi":"10.5802/aif.3545","DOIUrl":"https://doi.org/10.5802/aif.3545","url":null,"abstract":"Abstract : let k be a finite field of characteristic p>0, W(k) the ring of Witt vectors of k, X a smooth scheme over spec W(k) and X_0 the special fiber of X.In 1987, Deligne and Illusie proved the degeneration of the spectralsequence ``de Hodge vers de Rham'' in a purely algebraic way, by constructing aquasi-isomorphism at the level of derived categories between the de Rham complex of X_0 with a complex with 0 differentials. Simultaneously Fontaine and Messingconstructed a divided Frobenius map on the crystalline complexes associated with X_0. We show that bothmorphisms of derived categories are compatible mod p>0 if the dimension of X_0 is <p-1.We use this compatibility to compute the filtered phi-module mod,p associated to the Drinfeld Curve.Resume: Soit k un corps fini de caracteristique p>0, W(k) l'anneau des vecteurs de Witt de k, X un schema lisse sur spec W(k), X_0 la fibre speciale de X. En 1987, Deligne et Illusie ont demontre la degenerescence de la suitespectrale de Hodge vers de Rham d'une facon purement algebrique, en construisantun quasi-isomorphisme dans la categorie derivee entre le complexe de de Rham de X_0 et un complexe a differentielles nulles. Concomitamment, Fontaine et Messing ont construit un Frobenius divise sur les complexes cristallinsassocies a X_0. Nous montrons que ces deux morphismes de categories derivees sont compatibles. Comme application de cette compatibilite, nous donnons la structure du phi-module filtre mod p associe a la courbe de Drinfeld.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46745941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In his work on representations of Thompson's group $F$, Vaughan Jones defined and studied the $3$-colorable subgroup $mathcal{F}$ of $F$. Later, Ren showed that it is isomorphic with the Brown-Thompson group $F_4$. In this paper we continue with the study of the $3$-colorable subgroup and prove that the quasi-regular representation of $F$ associated with the $3$-colorable subgroup is irreducible. We show moreover that the preimage of $mathcal{F}$ under a certain injective endomorphism of $F$ is contained in three (explicit) maximal subgroups of $F$ of infinite index. These subgroups are different from the previously known infinite index maximal subgroups of $F$, namely the parabolic subgroups that fix a point in $(0,1)$, (up to isomorphism) the Jones' oriented subgroup $vec{F}$, and the explicit examples found by Golan.
{"title":"On the 3-colorable subgroup ℱ and maximal subgroups of Thompson’s group ","authors":"Valeriano Aiello, T. Nagnibeda","doi":"10.5802/aif.3555","DOIUrl":"https://doi.org/10.5802/aif.3555","url":null,"abstract":"In his work on representations of Thompson's group $F$, Vaughan Jones defined and studied the $3$-colorable subgroup $mathcal{F}$ of $F$. Later, Ren showed that it is isomorphic with the Brown-Thompson group $F_4$. In this paper we continue with the study of the $3$-colorable subgroup and prove that the quasi-regular representation of $F$ associated with the $3$-colorable subgroup is irreducible. We show moreover that the preimage of $mathcal{F}$ under a certain injective endomorphism of $F$ is contained in three (explicit) maximal subgroups of $F$ of infinite index. These subgroups are different from the previously known infinite index maximal subgroups of $F$, namely the parabolic subgroups that fix a point in $(0,1)$, (up to isomorphism) the Jones' oriented subgroup $vec{F}$, and the explicit examples found by Golan.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71210550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Córdoba’s differentiation theorem: revisited","authors":"Ángel D. Martínez","doi":"10.5802/aif.3535","DOIUrl":"https://doi.org/10.5802/aif.3535","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49625918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"BMO solutions to quasilinear equations of p-Laplace type","authors":"N. Phuc, I. Verbitsky","doi":"10.5802/aif.3485","DOIUrl":"https://doi.org/10.5802/aif.3485","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42034778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The missing (A,D,r) diagram","authors":"Alexandre Delyon, Antoine Henrot, Y. Privat","doi":"10.5802/aif.3484","DOIUrl":"https://doi.org/10.5802/aif.3484","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49570697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The leading coefficient of the L 2 -Alexander torsion","authors":"Fathi Ben Aribi, Stefan Friedl, G. Herrmann","doi":"10.5802/aif.3509","DOIUrl":"https://doi.org/10.5802/aif.3509","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44431845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On quotients of ℳ ¯","authors":"Irene Schwarz","doi":"10.5802/aif.3496","DOIUrl":"https://doi.org/10.5802/aif.3496","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49600779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A class formula for L-series in positive characteristic","authors":"F. Demeslay","doi":"10.5802/aif.3512","DOIUrl":"https://doi.org/10.5802/aif.3512","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45561385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Hartogs extension theorem for unbounded domains in ℂ n ","authors":"A. Boggess, R. Dwilewicz, E. Porten","doi":"10.5802/aif.3514","DOIUrl":"https://doi.org/10.5802/aif.3514","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45747799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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