Local Arboreal Representations
Let K be a field complete with respect to a discrete valuation v of residue characteristic p. Let f(z)∈K[z] be a separable polynomial of the form z[superscript ℓ]−c. Given a∈K, we examine the Galois groups and ramification groups of the extensions of K generated by the solutions to fn(z)=a. The beha...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Published: |
Oxford University Press (OUP)
2018
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| Online Access: | http://hdl.handle.net/1721.1/116023 https://orcid.org/0000-0002-8593-2792 |
| _version_ | 1811075474061787136 |
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| author | Anderson, Jacqueline Hamblen, Spencer Poonen, Bjorn Walton, Laura |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Anderson, Jacqueline Hamblen, Spencer Poonen, Bjorn Walton, Laura |
| author_sort | Anderson, Jacqueline |
| collection | MIT |
| description | Let K be a field complete with respect to a discrete valuation v of residue characteristic p. Let f(z)∈K[z] be a separable polynomial of the form z[superscript ℓ]−c. Given a∈K, we examine the Galois groups and ramification groups of the extensions of K generated by the solutions to fn(z)=a. The behavior depends upon v(c), and we find that it shifts dramatically as v(c) crosses a certain value:
0 in the case p∤ℓ, and −p/(p−1) in the case p=ℓ. |
| first_indexed | 2024-09-23T10:06:41Z |
| format | Article |
| id | mit-1721.1/116023 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T10:06:41Z |
| publishDate | 2018 |
| publisher | Oxford University Press (OUP) |
| record_format | dspace |
| spelling | mit-1721.1/1160232022-09-26T15:46:42Z Local Arboreal Representations Anderson, Jacqueline Hamblen, Spencer Poonen, Bjorn Walton, Laura Massachusetts Institute of Technology. Department of Mathematics Poonen, Bjorn Let K be a field complete with respect to a discrete valuation v of residue characteristic p. Let f(z)∈K[z] be a separable polynomial of the form z[superscript ℓ]−c. Given a∈K, we examine the Galois groups and ramification groups of the extensions of K generated by the solutions to fn(z)=a. The behavior depends upon v(c), and we find that it shifts dramatically as v(c) crosses a certain value: 0 in the case p∤ℓ, and −p/(p−1) in the case p=ℓ. 2018-05-31T17:20:39Z 2018-05-31T17:20:39Z 2017-02 2017-01 2018-05-29T17:28:05Z Article http://purl.org/eprint/type/JournalArticle 1073-7928 1687-0247 http://hdl.handle.net/1721.1/116023 Anderson, Jacqueline et al. “Local Arboreal Representations.” International Mathematics Research Notices (March 2017): 1-21 © 2017 The Authors https://orcid.org/0000-0002-8593-2792 http://dx.doi.org/10.1093/IMRN/RNX054 International Mathematics Research Notices Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press (OUP) arXiv |
| spellingShingle | Anderson, Jacqueline Hamblen, Spencer Poonen, Bjorn Walton, Laura Local Arboreal Representations |
| title | Local Arboreal Representations |
| title_full | Local Arboreal Representations |
| title_fullStr | Local Arboreal Representations |
| title_full_unstemmed | Local Arboreal Representations |
| title_short | Local Arboreal Representations |
| title_sort | local arboreal representations |
| url | http://hdl.handle.net/1721.1/116023 https://orcid.org/0000-0002-8593-2792 |
| work_keys_str_mv | AT andersonjacqueline localarborealrepresentations AT hamblenspencer localarborealrepresentations AT poonenbjorn localarborealrepresentations AT waltonlaura localarborealrepresentations |