Pub Date : 2023-03-01DOI: 10.1017/s1474748023000051
{"title":"JMJ volume 22 issue 2 Cover and Front matter","authors":"","doi":"10.1017/s1474748023000051","DOIUrl":"https://doi.org/10.1017/s1474748023000051","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":" ","pages":"f1 - f2"},"PeriodicalIF":0.9,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49417751","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 : 2023-01-01DOI: 10.1017/s1474748023000038
{"title":"JMJ volume 22 issue 1 Cover and Front matter","authors":"","doi":"10.1017/s1474748023000038","DOIUrl":"https://doi.org/10.1017/s1474748023000038","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":" ","pages":"f1 - f2"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47576544","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 : 2023-01-01DOI: 10.1017/s147474802300004x
{"title":"JMJ volume 22 issue 1 Cover and Back matter","authors":"","doi":"10.1017/s147474802300004x","DOIUrl":"https://doi.org/10.1017/s147474802300004x","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":" ","pages":"b1 - b2"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45414089","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 : 2022-12-06DOI: 10.1017/s1474748022000524
S. Lichtenbaum
We formulate a conjecture on the special values of zeta functions of regular arithmetic schemes in terms of Weil-étale cohomology…
根据Weilétale上同调，我们给出了正则算术格式zeta函数特殊值的一个猜想…
{"title":"SPECIAL VALUES OF ZETA-FUNCTIONS OF REGULAR SCHEMES","authors":"S. Lichtenbaum","doi":"10.1017/s1474748022000524","DOIUrl":"https://doi.org/10.1017/s1474748022000524","url":null,"abstract":"\u0000 We formulate a conjecture on the special values of zeta functions of regular arithmetic schemes in terms of Weil-étale cohomology…","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47952591","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 : 2022-11-10DOI: 10.1017/s1474748022000536
Giovanni Italiano, Bruno Martelli, Matteo Migliorini
We construct some cusped finite-volume hyperbolic <jats:italic>n</jats:italic>-manifolds <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000536_inline1.png" /> <jats:tex-math> $M^n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> that fibre algebraically in all the dimensions <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000536_inline2.png" /> <jats:tex-math> $5leq n leq 8$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. That is, there is a surjective homomorphism <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000536_inline3.png" /> <jats:tex-math> $pi _1(M^n) to {mathbb {Z}}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with finitely generated kernel. The kernel is also finitely presented in the dimensions <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000536_inline4.png" /> <jats:tex-math> $n=7, 8$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, and this leads to the first examples of hyperbolic <jats:italic>n</jats:italic>-manifolds <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000536_inline5.png" /> <jats:tex-math> $widetilde M^n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> whose fundamental group is finitely presented but not of finite type. These <jats:italic>n</jats:italic>-manifolds <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000536_inline6.png" /> <jats:tex-math> $widetilde M^n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> have infinitely many cusps of maximal rank and, hence, infinite Betti number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000536_inline7.png" /> <jats:tex-math> $b_{n-1}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. They cover the finite-volume manifold <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000536_inline8.png" /> <jats:tex-math> $M^n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. We obtain these examples by assigning some appropriate <jats:italic>colours</jats:italic> and <jats:italic>states</jats:italic> to a family of right-angled hyperbolic polytopes <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S14
我们构造了一些在所有维度$5leq n leq 8$上都具有代数纤维的顶形有限体积双曲n流形$M^n$。即存在一个有限生成核的满射同态$pi _1(M^n) to {mathbb {Z}}$。核也在维度$n=7, 8$中有限地表示，这导致了双曲n流形$widetilde M^n$的第一个例子，其基本群是有限地表示的，但不是有限类型。这些n流形$widetilde M^n$有无穷多个最大秩顶点，因此有无穷个Betti数$b_{n-1}$。它们涵盖了有限体积的歧管$M^n$。我们通过给一组直角双曲多面体$P^5, ldots , P^8$分配一些适当的颜色和状态，然后应用Jankiewicz, Norin和Wise[18]和Bestvina和Brady[7]的一些论点得到这些例子。我们以一种重要的方式利用了Gosset多面体对偶$P^n$的显著性质，以及关键维$n=7,8$的积分八元代数。
{"title":"HYPERBOLIC MANIFOLDS THAT FIBRE ALGEBRAICALLY UP TO DIMENSION 8","authors":"Giovanni Italiano, Bruno Martelli, Matteo Migliorini","doi":"10.1017/s1474748022000536","DOIUrl":"https://doi.org/10.1017/s1474748022000536","url":null,"abstract":"We construct some cusped finite-volume hyperbolic <jats:italic>n</jats:italic>-manifolds <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000536_inline1.png\" /> <jats:tex-math> $M^n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> that fibre algebraically in all the dimensions <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000536_inline2.png\" /> <jats:tex-math> $5leq n leq 8$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. That is, there is a surjective homomorphism <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000536_inline3.png\" /> <jats:tex-math> $pi _1(M^n) to {mathbb {Z}}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with finitely generated kernel. The kernel is also finitely presented in the dimensions <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000536_inline4.png\" /> <jats:tex-math> $n=7, 8$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, and this leads to the first examples of hyperbolic <jats:italic>n</jats:italic>-manifolds <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000536_inline5.png\" /> <jats:tex-math> $widetilde M^n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> whose fundamental group is finitely presented but not of finite type. These <jats:italic>n</jats:italic>-manifolds <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000536_inline6.png\" /> <jats:tex-math> $widetilde M^n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> have infinitely many cusps of maximal rank and, hence, infinite Betti number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000536_inline7.png\" /> <jats:tex-math> $b_{n-1}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. They cover the finite-volume manifold <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000536_inline8.png\" /> <jats:tex-math> $M^n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. We obtain these examples by assigning some appropriate <jats:italic>colours</jats:italic> and <jats:italic>states</jats:italic> to a family of right-angled hyperbolic polytopes <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S14","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"1366 ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506282","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 : 2022-11-01DOI: 10.1017/s1474748022000512
{"title":"JMJ volume 21 issue 6 Cover and Back matter","authors":"","doi":"10.1017/s1474748022000512","DOIUrl":"https://doi.org/10.1017/s1474748022000512","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":" ","pages":"b1 - b2"},"PeriodicalIF":0.9,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47230188","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 : 2022-10-24DOI: 10.1017/s1474748022000457
Ariyan Javanpeykar, Daniel Loughran, Siddharth Mathur
We prove finiteness results for sets of varieties over number fields with good reduction outside a given finite set of places using cyclic covers. We obtain a version of the Shafarevich conjecture for weighted projective surfaces, double covers of abelian varieties and reduce the Shafarevich conjecture for hypersurfaces to the case of hypersurfaces of high dimension. These are special cases of a general setup for integral points on moduli stacks of cyclic covers, and our arithmetic results are achieved via a version of the Chevalley–Weil theorem for stacks.
{"title":"GOOD REDUCTION AND CYCLIC COVERS","authors":"Ariyan Javanpeykar, Daniel Loughran, Siddharth Mathur","doi":"10.1017/s1474748022000457","DOIUrl":"https://doi.org/10.1017/s1474748022000457","url":null,"abstract":"We prove finiteness results for sets of varieties over number fields with good reduction outside a given finite set of places using cyclic covers. We obtain a version of the Shafarevich conjecture for weighted projective surfaces, double covers of abelian varieties and reduce the Shafarevich conjecture for hypersurfaces to the case of hypersurfaces of high dimension. These are special cases of a general setup for integral points on moduli stacks of cyclic covers, and our arithmetic results are achieved via a version of the Chevalley–Weil theorem for stacks.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"1340 ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506269","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 : 2022-10-24DOI: 10.1017/s1474748022000470
M. Bondarko
<jats:p>For a weight structure <jats:italic>w</jats:italic> on a triangulated category <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000470_inline1.png" /> <jats:tex-math> $underline {C}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> we prove that the corresponding <jats:italic>weight complex</jats:italic> functor and some other (<jats:italic>weight-exact</jats:italic>) functors are ‘conservative up to weight-degenerate objects’; this improves earlier conservativity formulations. In the case <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000470_inline2.png" /> <jats:tex-math> $w=w^{sph}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> (the <jats:italic>spherical</jats:italic> weight structure on <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000470_inline3.png" /> <jats:tex-math> $SH$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>), we deduce the following converse to the stable Hurewicz theorem: <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000470_inline4.png" /> <jats:tex-math> $H^{sing}_{i}(M)={0}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> for all <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000470_inline5.png" /> <jats:tex-math> $i<0$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> if and only if <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000470_inline6.png" /> <jats:tex-math> $Min SH$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is an extension of a connective spectrum by an acyclic one. We also prove an equivariant version of this statement.</jats:p> <jats:p>The main idea is to study <jats:italic>M</jats:italic> that has <jats:italic>no weights</jats:italic><jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000470_inline7.png" /> <jats:tex-math> $m,dots ,n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> (‘in the middle’). For <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748022000470_inline8.png" /> <jats:tex-math> $w=w^{sph}$ </jats:tex-math> </jats:alternatives>
对于三角范畴$dunderline｛C｝$上的权结构w，我们证明了相应的权复函子和其他一些（权精确）函子是“保守到权退化对象”；这改进了早期的保守性公式。在$w=w^{sph}$（$SH$上的球权结构）的情况下，我们推导出稳定Hurewicz定理的以下逆式：$H^{sing}_{i} 对于所有$i，（M）=｛0｝$当且仅当SH$中的$M是连接谱的非循环扩展。我们还证明了这一说法的一个模棱两可的版本。主要思想是研究没有权重$M，dots，n$（“在中间”）的M。对于$w=w^｛sph｝$，如果存在一个可分辨三角形$LM到M到RM$，则情况就是这样，其中$RM$是n连通谱，$LM$是Margolis定义意义上的（M的）$M-1$骨架；每当$H^{sing}_i（M） =$Mle ile n$和$H的｛0｝$^{sing}_{m-1}（m）$是一个自由阿贝尔群。我们还考虑了杀死权重$m，dots，n$的态射；那些“把n-w-skeleta变成$m-1$-w-seleta”。
{"title":"ON MORPHISMS KILLING WEIGHTS AND STABLE HUREWICZ-TYPE THEOREMS","authors":"M. Bondarko","doi":"10.1017/s1474748022000470","DOIUrl":"https://doi.org/10.1017/s1474748022000470","url":null,"abstract":"\u0000\t <jats:p>For a weight structure <jats:italic>w</jats:italic> on a triangulated category <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000470_inline1.png\" />\u0000\t\t<jats:tex-math>\u0000$underline {C}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> we prove that the corresponding <jats:italic>weight complex</jats:italic> functor and some other (<jats:italic>weight-exact</jats:italic>) functors are ‘conservative up to weight-degenerate objects’; this improves earlier conservativity formulations. In the case <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000470_inline2.png\" />\u0000\t\t<jats:tex-math>\u0000$w=w^{sph}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> (the <jats:italic>spherical</jats:italic> weight structure on <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000470_inline3.png\" />\u0000\t\t<jats:tex-math>\u0000$SH$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>), we deduce the following converse to the stable Hurewicz theorem: <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000470_inline4.png\" />\u0000\t\t<jats:tex-math>\u0000$H^{sing}_{i}(M)={0}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> for all <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000470_inline5.png\" />\u0000\t\t<jats:tex-math>\u0000$i<0$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> if and only if <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000470_inline6.png\" />\u0000\t\t<jats:tex-math>\u0000$Min SH$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> is an extension of a connective spectrum by an acyclic one. We also prove an equivariant version of this statement.</jats:p>\u0000\t <jats:p>The main idea is to study <jats:italic>M</jats:italic> that has <jats:italic>no weights</jats:italic><jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000470_inline7.png\" />\u0000\t\t<jats:tex-math>\u0000$m,dots ,n$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> (‘in the middle’). For <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748022000470_inline8.png\" />\u0000\t\t<jats:tex-math>\u0000$w=w^{sph}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49382175","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 : 2022-09-28DOI: 10.1017/s1474748022000469
Thomas H. Geisser, B. Morin
We define cohomological complexes of locally compact abelian groups associated with varieties over p-adic fields and prove a duality theorem under some assumption. Our duality takes the form of Pontryagin duality between locally compact motivic cohomology groups.
{"title":"PONTRYAGIN DUALITY FOR VARIETIES OVER p-ADIC FIELDS","authors":"Thomas H. Geisser, B. Morin","doi":"10.1017/s1474748022000469","DOIUrl":"https://doi.org/10.1017/s1474748022000469","url":null,"abstract":"\u0000 We define cohomological complexes of locally compact abelian groups associated with varieties over p-adic fields and prove a duality theorem under some assumption. Our duality takes the form of Pontryagin duality between locally compact motivic cohomology groups.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44682320","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 : 2022-09-26DOI: 10.1017/s1474748023000178
J. Hornbostel, Doosung Park
We prove that real topological Hochschild homology $mathrm {THR}$ for schemes with involution satisfies base change and descent for the ${mathbb {Z}/2}$ -isovariant étale topology. As an application, we provide computations for the projective line (with and without involution) and the higher-dimensional projective spaces.
{"title":"REAL TOPOLOGICAL HOCHSCHILD HOMOLOGY OF SCHEMES","authors":"J. Hornbostel, Doosung Park","doi":"10.1017/s1474748023000178","DOIUrl":"https://doi.org/10.1017/s1474748023000178","url":null,"abstract":"\u0000 We prove that real topological Hochschild homology \u0000 \u0000 \u0000 \u0000$mathrm {THR}$\u0000\u0000 \u0000 for schemes with involution satisfies base change and descent for the \u0000 \u0000 \u0000 \u0000${mathbb {Z}/2}$\u0000\u0000 \u0000 -isovariant étale topology. As an application, we provide computations for the projective line (with and without involution) and the higher-dimensional projective spaces.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44081435","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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