Pub Date : 2023-11-06DOI: 10.1017/s1474748023000361
Wodson Mendson, Jorge Vitório Pereira
Abstract We investigate the geometry of codimension one foliations on smooth projective varieties defined over fields of positive characteristic with an eye toward applications to the structure of codimension one holomorphic foliations on projective manifolds.
{"title":"CODIMENSION ONE FOLIATIONS IN POSITIVE CHARACTERISTIC","authors":"Wodson Mendson, Jorge Vitório Pereira","doi":"10.1017/s1474748023000361","DOIUrl":"https://doi.org/10.1017/s1474748023000361","url":null,"abstract":"Abstract We investigate the geometry of codimension one foliations on smooth projective varieties defined over fields of positive characteristic with an eye toward applications to the structure of codimension one holomorphic foliations on projective manifolds.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135635353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-06DOI: 10.1017/s1474748023000373
Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim
Abstract We investigate the translation lengths of group elements that arise in random walks on the isometry groups of Gromov hyperbolic spaces. In particular, without any moment condition, we prove that non-elementary random walks exhibit at least linear growth of translation lengths. As a corollary, almost every random walk on mapping class groups eventually becomes pseudo-Anosov, and almost every random walk on $mathrm {Out}(F_n)$ eventually becomes fully irreducible. If the underlying measure further has finite first moment, then the growth rate of translation lengths is equal to the drift, the escape rate of the random walk. We then apply our technique to investigate the random walks induced by the action of mapping class groups on Teichmüller spaces. In particular, we prove the spectral theorem under finite first moment condition, generalizing a result of Dahmani and Horbez.
{"title":"LINEAR GROWTH OF TRANSLATION LENGTHS OF RANDOM ISOMETRIES ON GROMOV HYPERBOLIC SPACES AND TEICHMÜLLER SPACES","authors":"Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim","doi":"10.1017/s1474748023000373","DOIUrl":"https://doi.org/10.1017/s1474748023000373","url":null,"abstract":"Abstract We investigate the translation lengths of group elements that arise in random walks on the isometry groups of Gromov hyperbolic spaces. In particular, without any moment condition, we prove that non-elementary random walks exhibit at least linear growth of translation lengths. As a corollary, almost every random walk on mapping class groups eventually becomes pseudo-Anosov, and almost every random walk on $mathrm {Out}(F_n)$ eventually becomes fully irreducible. If the underlying measure further has finite first moment, then the growth rate of translation lengths is equal to the drift, the escape rate of the random walk. We then apply our technique to investigate the random walks induced by the action of mapping class groups on Teichmüller spaces. In particular, we prove the spectral theorem under finite first moment condition, generalizing a result of Dahmani and Horbez.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135544884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-17DOI: 10.1017/s1474748023000348
Bingrong Huang
Abstract In this paper, we prove uniform bounds for $operatorname {GL}(3)times operatorname {GL}(2) L$ -functions in the $operatorname {GL}(2)$ spectral aspect and the t aspect by a delta method. More precisely, let $phi $ be a Hecke–Maass cusp form for $operatorname {SL}(3,mathbb {Z})$ and f a Hecke–Maass cusp form for $operatorname {SL}(2,mathbb {Z})$ with the spectral parameter $t_f$ . Then for $tin mathbb {R}$ and any $varepsilon>0$ , we have $$begin{align*}L(1/2+it,phitimes f) ll_{phi,varepsilon} (t_f+|t|)^{27/20+varepsilon}. end{align*}$$ Moreover, we get subconvexity bounds for $L(1/2+it,phi times f)$ whenever $|t|-t_f gg (|t|+t_f)^{3/5+varepsilon }$ .
{"title":"UNIFORM BOUNDS FOR <i>L</i>-FUNCTIONS","authors":"Bingrong Huang","doi":"10.1017/s1474748023000348","DOIUrl":"https://doi.org/10.1017/s1474748023000348","url":null,"abstract":"Abstract In this paper, we prove uniform bounds for $operatorname {GL}(3)times operatorname {GL}(2) L$ -functions in the $operatorname {GL}(2)$ spectral aspect and the t aspect by a delta method. More precisely, let $phi $ be a Hecke–Maass cusp form for $operatorname {SL}(3,mathbb {Z})$ and f a Hecke–Maass cusp form for $operatorname {SL}(2,mathbb {Z})$ with the spectral parameter $t_f$ . Then for $tin mathbb {R}$ and any $varepsilon>0$ , we have $$begin{align*}L(1/2+it,phitimes f) ll_{phi,varepsilon} (t_f+|t|)^{27/20+varepsilon}. end{align*}$$ Moreover, we get subconvexity bounds for $L(1/2+it,phi times f)$ whenever $|t|-t_f gg (|t|+t_f)^{3/5+varepsilon }$ .","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135993093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1017/s1474748023000336
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
{"title":"JMJ volume 22 issue 6 Cover and Back matter","authors":"","doi":"10.1017/s1474748023000336","DOIUrl":"https://doi.org/10.1017/s1474748023000336","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1017/s1474748023000324
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
{"title":"JMJ volume 22 issue 6 Cover and Front matter","authors":"","doi":"10.1017/s1474748023000324","DOIUrl":"https://doi.org/10.1017/s1474748023000324","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135924891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-10DOI: 10.1017/s1474748023000300
Fritz Hörmann
Abstract We axiomatise the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalised automorphic sheaf is proposed which includes sheaves of (meromorphic) sections of automorphic vector bundles with prescribed vanishing and pole orders along strata in the compactification, and their quotients. These include, for instance, sheaves of Jacobi forms and weakly holomorphic modular forms. Using this machinery, we give a short and purely algebraic proof of the proportionality theorem of Hirzebruch and Mumford.
{"title":"GENERALISED AUTOMORPHIC SHEAVES AND THE PROPORTIONALITY PRINCIPLE OF HIRZEBRUCH-MUMFORD","authors":"Fritz Hörmann","doi":"10.1017/s1474748023000300","DOIUrl":"https://doi.org/10.1017/s1474748023000300","url":null,"abstract":"Abstract We axiomatise the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalised automorphic sheaf is proposed which includes sheaves of (meromorphic) sections of automorphic vector bundles with prescribed vanishing and pole orders along strata in the compactification, and their quotients. These include, for instance, sheaves of Jacobi forms and weakly holomorphic modular forms. Using this machinery, we give a short and purely algebraic proof of the proportionality theorem of Hirzebruch and Mumford.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136296130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-09DOI: 10.1017/s1474748023000269
{"title":"JMJ volume 22 issue 5 Cover and Front matter","authors":"","doi":"10.1017/s1474748023000269","DOIUrl":"https://doi.org/10.1017/s1474748023000269","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47726178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-09DOI: 10.1017/s1474748023000270
{"title":"JMJ volume 22 issue 5 Cover and Back matter","authors":"","doi":"10.1017/s1474748023000270","DOIUrl":"https://doi.org/10.1017/s1474748023000270","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49359665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-17DOI: 10.1017/s147474802300021x
Ashay A. Burungale, Shin-ichi Kobayashi, Kazuto Ota
Let K be an imaginary quadratic field and $pgeq 5$ a rational prime inert in K. For a $mathbb {Q}$ -curve E with complex multiplication by $mathcal {O}_K$ and good reduction at p, K. Rubin introduced a p-adic L-function $mathscr {L}_{E}$ which interpolates special values of L-functions of E twisted by anticyclotomic characters of K. In this paper, we prove a formula which links certain values of $mathscr {L}_{E}$ outside its defining range of interpolation with rational points on E. Arithmetic consequences include p-converse to the Gross–Zagier and Kolyvagin theorem for E.A key tool of the proof is the recent resolution of Rubin’s conjecture on the structure of local units in the anticyclotomic ${mathbb {Z}}_p$ -extension $Psi _infty $ of
{"title":"p-ADIC L-FUNCTIONS AND RATIONAL POINTS ON CM ELLIPTIC CURVES AT INERT PRIMES","authors":"Ashay A. Burungale, Shin-ichi Kobayashi, Kazuto Ota","doi":"10.1017/s147474802300021x","DOIUrl":"https://doi.org/10.1017/s147474802300021x","url":null,"abstract":"\u0000\t <jats:p>Let <jats:italic>K</jats:italic> be an imaginary quadratic field and <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S147474802300021X_inline1.png\" />\u0000\t\t<jats:tex-math>\u0000$pgeq 5$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> a rational prime inert in <jats:italic>K</jats:italic>. For a <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S147474802300021X_inline2.png\" />\u0000\t\t<jats:tex-math>\u0000$mathbb {Q}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>-curve <jats:italic>E</jats:italic> with complex multiplication by <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S147474802300021X_inline3.png\" />\u0000\t\t<jats:tex-math>\u0000$mathcal {O}_K$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> and good reduction at <jats:italic>p</jats:italic>, K. Rubin introduced a <jats:italic>p</jats:italic>-adic <jats:italic>L</jats:italic>-function <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S147474802300021X_inline4.png\" />\u0000\t\t<jats:tex-math>\u0000$mathscr {L}_{E}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> which interpolates special values of <jats:italic>L</jats:italic>-functions of <jats:italic>E</jats:italic> twisted by anticyclotomic characters of <jats:italic>K</jats:italic>. In this paper, we prove a formula which links certain values of <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S147474802300021X_inline5.png\" />\u0000\t\t<jats:tex-math>\u0000$mathscr {L}_{E}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> outside its defining range of interpolation with rational points on <jats:italic>E</jats:italic>. Arithmetic consequences include <jats:italic>p</jats:italic>-converse to the Gross–Zagier and Kolyvagin theorem for <jats:italic>E</jats:italic>.</jats:p>\u0000\t <jats:p>A key tool of the proof is the recent resolution of Rubin’s conjecture on the structure of local units in the anticyclotomic <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S147474802300021X_inline6.png\" />\u0000\t\t<jats:tex-math>\u0000${mathbb {Z}}_p$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>-extension <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S147474802300021X_inline7.png\" />\u0000\t\t<jats:tex-math>\u0000$Psi _infty $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> of","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42628857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1017/s1474748023000257
{"title":"JMJ volume 22 issue 4 Cover and Back matter","authors":"","doi":"10.1017/s1474748023000257","DOIUrl":"https://doi.org/10.1017/s1474748023000257","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44984426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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