{"title":"On weighted-blowup formulae of genus zero orbifold Gromov–Witten invariants","authors":"Bohui Chen, Cheng-Yong Du","doi":"10.1112/S0010437X23007315","DOIUrl":"https://doi.org/10.1112/S0010437X23007315","url":null,"abstract":"In this paper, we provide a new approach to prove some weighted-blowup formulae for genus zero orbifold Gromov–Witten invariants. As a consequence, we show the invariance of symplectically rational connectedness with respect to weighted-blowup along positive centers. Furthermore, we use this method to give a new proof to the genus zero relative-orbifold correspondence of Gromov–Witten invariants.","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"159 1","pages":"1833 - 1871"},"PeriodicalIF":1.8,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44428608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the u∞-torsion submodule of prismatic cohomology","authors":"Shizhang Li, Tongyin Liu","doi":"10.1112/S0010437X23007261","DOIUrl":"https://doi.org/10.1112/S0010437X23007261","url":null,"abstract":"We investigate the maximal finite length submodule of the Breuil–Kisin prismatic cohomology of a smooth proper formal scheme over a $p$-adic ring of integers. This submodule governs pathology phenomena in integral $p$-adic cohomology theories. Geometric applications include a control, in low degrees and mild ramifications, of (1) the discrepancy between two naturally associated Albanese varieties in characteristic $p$, and (2) the kernel of the specialization map in $p$-adic étale cohomology. As an arithmetic application, we study the boundary case of the theory due to Fontaine and Laffaille, Fontaine and Messing, and Kato. Also included is an interesting example, generalized from a construction in Bhatt, Morrow and Scholze's work, which illustrates some of our theoretical results being sharp, and negates a question of Breuil.","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"159 1","pages":"1607 - 1672"},"PeriodicalIF":1.8,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45924815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Isometric actions on Lp-spaces: dependence on the value of p","authors":"A. Marrakchi, Mikael de la Salle","doi":"10.1112/S0010437X23007121","DOIUrl":"https://doi.org/10.1112/S0010437X23007121","url":null,"abstract":"Answering a question by Chatterji–Druţu–Haglund, we prove that, for every locally compact group $G$, there exists a critical constant $p_G in [0,infty ]$ such that $G$ admits a continuous affine isometric action on an $L_p$ space ($0< p<infty$) with unbounded orbits if and only if $p geq p_G$. A similar result holds for the existence of proper continuous affine isometric actions on $L_p$ spaces. Using a representation of cohomology by harmonic cocycles, we also show that such unbounded orbits cannot occur when the linear part comes from a measure-preserving action, or more generally a state-preserving action on a von Neumann algebra and $p>2$. We also prove the stability of this critical constant $p_G$ under $L_p$ measure equivalence, answering a question of Fisher.","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"159 1","pages":"1300 - 1313"},"PeriodicalIF":1.8,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45788360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A letter from the Editors","authors":"","doi":"10.1112/s0010437x23007248","DOIUrl":"https://doi.org/10.1112/s0010437x23007248","url":null,"abstract":"An abstract is not available for this content. As you have access to this content, full HTML content is provided on this page. A PDF of this content is also available in through the ‘Save PDF’ action button.","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135288564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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