{"title":"半稳定约简Abelian变种的Tate模上的伽罗瓦作用","authors":"Khai-Hoan Nguyen-Dang","doi":"10.1016/j.jnt.2024.08.008","DOIUrl":null,"url":null,"abstract":"<div><div>Let <em>p</em> be a rational prime number, let <em>K</em> denote a finite extension of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>, <span><math><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></math></span> some fixed algebraic closure of <em>K</em>. Let <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> be the absolute Galois group of <em>K</em> and let <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>K</mi></mrow></msub><mo>⊂</mo><msub><mrow><mi>G</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> be its inertial subgroup. Let <em>A</em> be an Abelian variety defined over <em>K</em>, with semi-stable reduction. In this note, we give a criterion for which <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><msup><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow></msup><mo>=</mo><mn>0</mn></math></span>, where <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is the <em>p</em>-adic Tate module associated to <em>A</em>.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"269 ","pages":"Pages 247-259"},"PeriodicalIF":0.6000,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Galois actions on Tate modules of Abelian varieties with semi-stable reduction\",\"authors\":\"Khai-Hoan Nguyen-Dang\",\"doi\":\"10.1016/j.jnt.2024.08.008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <em>p</em> be a rational prime number, let <em>K</em> denote a finite extension of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>, <span><math><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></math></span> some fixed algebraic closure of <em>K</em>. Let <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> be the absolute Galois group of <em>K</em> and let <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>K</mi></mrow></msub><mo>⊂</mo><msub><mrow><mi>G</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> be its inertial subgroup. Let <em>A</em> be an Abelian variety defined over <em>K</em>, with semi-stable reduction. In this note, we give a criterion for which <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><msup><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow></msup><mo>=</mo><mn>0</mn></math></span>, where <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is the <em>p</em>-adic Tate module associated to <em>A</em>.</div></div>\",\"PeriodicalId\":50110,\"journal\":{\"name\":\"Journal of Number Theory\",\"volume\":\"269 \",\"pages\":\"Pages 247-259\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022314X2400218X\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X2400218X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Galois actions on Tate modules of Abelian varieties with semi-stable reduction
Let p be a rational prime number, let K denote a finite extension of , some fixed algebraic closure of K. Let be the absolute Galois group of K and let be its inertial subgroup. Let A be an Abelian variety defined over K, with semi-stable reduction. In this note, we give a criterion for which , where is the p-adic Tate module associated to A.
期刊介绍：
The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field.
The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory.
Starting in May 2019, JNT will have a new format with 3 sections:
JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access.
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