Local Arboreal Representations
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1610.04969.pdf
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Author(s)
Anderson, Jacqueline
Hamblen, Spencer
Poonen, Bjorn
Walton, Laura
Date Issued
February 2017
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Citation
Anderson, Jacqueline et al. “Local Arboreal Representations.” International Mathematics Research Notices (March 2017): 1-21 © 2017 The Authors
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/IMRN/RNX054
