极限键多项式

IF 0.6 Q3 MATHEMATICS

Illinois Journal of Mathematics Pub Date : 2020-12-01 DOI:10.1215/00192082-8827671

Maria Alberich-Carramiñana, Alberto F. Boix, Julio Fernández, J. Guàrdia, E. Nart, J. Roé

{"title":"极限键多项式","authors":"Maria Alberich-Carramiñana, Alberto F. Boix, Julio Fernández, J. Guàrdia, E. Nart, J. Roé","doi":"10.1215/00192082-8827671","DOIUrl":null,"url":null,"abstract":"Let ν be a valuation of arbitrary rank on the polynomial ring K[x] with coefficients in a field K. We prove comparison theorems between MacLane–Vaquie key polynomials for valuations μ≤ν and abstract key polynomials for ν. Also, some results on invariants associated to limit key polynomials are obtained. In particular, if char(K)=0, we show that all the limit key polynomials of unbounded continuous families of augmentations have the numerical character equal to one.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"65 1","pages":"201-229"},"PeriodicalIF":0.6000,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Of limit key polynomials\",\"authors\":\"Maria Alberich-Carramiñana, Alberto F. Boix, Julio Fernández, J. Guàrdia, E. Nart, J. Roé\",\"doi\":\"10.1215/00192082-8827671\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let ν be a valuation of arbitrary rank on the polynomial ring K[x] with coefficients in a field K. We prove comparison theorems between MacLane–Vaquie key polynomials for valuations μ≤ν and abstract key polynomials for ν. Also, some results on invariants associated to limit key polynomials are obtained. In particular, if char(K)=0, we show that all the limit key polynomials of unbounded continuous families of augmentations have the numerical character equal to one.\",\"PeriodicalId\":56298,\"journal\":{\"name\":\"Illinois Journal of Mathematics\",\"volume\":\"65 1\",\"pages\":\"201-229\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Illinois Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1215/00192082-8827671\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Illinois Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1215/00192082-8827671","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 10

摘要

设Γ是域K中具有系数的多项式环K[x]上任意秩的一个估值。我们证明了估值μ≤Γ的MacLane–Vaquie密钥多项式与估值Γ的抽象密钥多项式之间的比较定理。此外，还得到了与极限键多项式相关的不变量的一些结果。特别地，如果char（K）=0，我们证明了无界连续增广族的所有极限键多项式都具有等于1的数值特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Of limit key polynomials

Let ν be a valuation of arbitrary rank on the polynomial ring K[x] with coefficients in a field K. We prove comparison theorems between MacLane–Vaquie key polynomials for valuations μ≤ν and abstract key polynomials for ν. Also, some results on invariants associated to limit key polynomials are obtained. In particular, if char(K)=0, we show that all the limit key polynomials of unbounded continuous families of augmentations have the numerical character equal to one.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Illinois Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： IJM strives to publish high quality research papers in all areas of mainstream mathematics that are of interest to a substantial number of its readers. IJM is published by Duke University Press on behalf of the Department of Mathematics at the University of Illinois at Urbana-Champaign.