{"title":"Parametrizations of subsets of the space of valuations","authors":"Josnei Novacoski, Caio Henrique Silva de Souza","doi":"10.1007/s00209-024-03554-0","DOIUrl":null,"url":null,"abstract":"<p>In this paper we present different ways to parametrize subsets of the space of valuations on <i>K</i>[<i>x</i>] extending a given valuation on <i>K</i>. We discuss the methods using pseudo-Cauchy sequences and approximation types. The method presented here is slightly different than the ones in the literature and we believe that our approach is more accurate.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"17 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Zeitschrift","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00209-024-03554-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper we present different ways to parametrize subsets of the space of valuations on K[x] extending a given valuation on K. We discuss the methods using pseudo-Cauchy sequences and approximation types. The method presented here is slightly different than the ones in the literature and we believe that our approach is more accurate.
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