Local Arboreal Representations
Author(s)Anderson, Jacqueline; Hamblen, Spencer; Poonen, Bjorn; Walton, Laura
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
International Mathematics Research Notices
Oxford University Press (OUP)
Anderson, Jacqueline et al. “Local Arboreal Representations.” International Mathematics Research Notices (March 2017): 1-21 © 2017 The Authors