Berkovich spaces embed in Euclidean spaces
Let K be a field that is complete with respect to a nonarchimedean absolute value such that K has a countable dense subset. We prove that the Berkovich analytification V[superscript an] of any d-dimensional quasi-projective scheme V over K embeds in R[superscrip 2d+1]. If, moreover, the value group...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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European Mathematical Society Publishing House
2017
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| Online Access: | http://hdl.handle.net/1721.1/106202 https://orcid.org/0000-0002-8593-2792 |
| _version_ | 1826198479563653120 |
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| author | Hrushovski, Ehud Loeser, François Poonen, Bjorn |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Hrushovski, Ehud Loeser, François Poonen, Bjorn |
| author_sort | Hrushovski, Ehud |
| collection | MIT |
| description | Let K be a field that is complete with respect to a nonarchimedean absolute value such that K has a countable dense subset. We prove that the Berkovich analytification V[superscript an] of any d-dimensional quasi-projective scheme V over K embeds in R[superscrip 2d+1]. If, moreover, the value group of K is dense in R>0 and V is a curve, then we describe the homeomorphism type of V[superscript an] by using the theory of local dendrites. |
| first_indexed | 2024-09-23T11:05:36Z |
| format | Article |
| id | mit-1721.1/106202 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:05:36Z |
| publishDate | 2017 |
| publisher | European Mathematical Society Publishing House |
| record_format | dspace |
| spelling | mit-1721.1/1062022022-09-27T17:06:27Z Berkovich spaces embed in Euclidean spaces Hrushovski, Ehud Loeser, François Poonen, Bjorn Massachusetts Institute of Technology. Department of Mathematics Poonen, Bjorn Let K be a field that is complete with respect to a nonarchimedean absolute value such that K has a countable dense subset. We prove that the Berkovich analytification V[superscript an] of any d-dimensional quasi-projective scheme V over K embeds in R[superscrip 2d+1]. If, moreover, the value group of K is dense in R>0 and V is a curve, then we describe the homeomorphism type of V[superscript an] by using the theory of local dendrites. 2017-01-05T16:08:19Z 2017-01-05T16:08:19Z 2014 Article http://purl.org/eprint/type/JournalArticle 0013-8584 http://hdl.handle.net/1721.1/106202 Hrushovski, Ehud, François Loeser, and Bjorn Poonen. “Berkovich Spaces Embed in Euclidean Spaces.” L’Enseignement Mathématique 60.3 (2014): 273–292. https://orcid.org/0000-0002-8593-2792 en_US http://dx.doi.org/10.4171/LEM/60-3/4-4 L’Enseignement Mathématique Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf European Mathematical Society Publishing House arXiv |
| spellingShingle | Hrushovski, Ehud Loeser, François Poonen, Bjorn Berkovich spaces embed in Euclidean spaces |
| title | Berkovich spaces embed in Euclidean spaces |
| title_full | Berkovich spaces embed in Euclidean spaces |
| title_fullStr | Berkovich spaces embed in Euclidean spaces |
| title_full_unstemmed | Berkovich spaces embed in Euclidean spaces |
| title_short | Berkovich spaces embed in Euclidean spaces |
| title_sort | berkovich spaces embed in euclidean spaces |
| url | http://hdl.handle.net/1721.1/106202 https://orcid.org/0000-0002-8593-2792 |
| work_keys_str_mv | AT hrushovskiehud berkovichspacesembedineuclideanspaces AT loeserfrancois berkovichspacesembedineuclideanspaces AT poonenbjorn berkovichspacesembedineuclideanspaces |