{"title":"Ax–Schanuel for variations of mixed Hodge structures","authors":"Kenneth Chung Tak Chiu","doi":"10.1007/s00208-024-02958-x","DOIUrl":null,"url":null,"abstract":"<p>We give properties of the real-split retraction of the mixed weak Mumford–Tate domain and prove the Ax–Schanuel property of period mappings arising from variations of mixed Hodge structures. An ingredient in the proof is the definability of the mixed period mapping obtained by Bakker–Brunebarbe–Klingler–Tsimerman. In comparison with preceding results, in the point counting step, we count rational points on definable quotients instead.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Annalen","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00208-024-02958-x","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We give properties of the real-split retraction of the mixed weak Mumford–Tate domain and prove the Ax–Schanuel property of period mappings arising from variations of mixed Hodge structures. An ingredient in the proof is the definability of the mixed period mapping obtained by Bakker–Brunebarbe–Klingler–Tsimerman. In comparison with preceding results, in the point counting step, we count rational points on definable quotients instead.
期刊介绍：
Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin.
The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin.
Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.
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