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2017 A new equivariant in nonarchimedean dynamics
Robert Rumely
Algebra Number Theory 11(4): 841-884 (2017). DOI: 10.2140/ant.2017.11.841

Abstract

Let K be a complete, algebraically closed nonarchimedean valued field, and let φ(z) K(z) have degree d 2. We show there is a canonical way to assign nonnegative integer weights wφ(P) to points of the Berkovich projective line over K in such a way that Pwφ(P) = d 1. When φ has bad reduction, the set of points with nonzero weight forms a distributed analogue of the unique point which occurs when φ has potential good reduction. Using this, we characterize the minimal resultant locus of φ in analytic and moduli-theoretic terms: analytically, it is the barycenter of the weight-measure associated to φ; moduli-theoretically, it is the closure of the set of points where φ has semistable reduction, in the sense of geometric invariant theory.

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Robert Rumely. "A new equivariant in nonarchimedean dynamics." Algebra Number Theory 11 (4) 841 - 884, 2017. https://doi.org/10.2140/ant.2017.11.841

Information

Received: 27 August 2015; Revised: 13 January 2017; Accepted: 11 February 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06735373
MathSciNet: MR3665639
Digital Object Identifier: 10.2140/ant.2017.11.841

Subjects:
Primary: 37P50
Secondary: 11S82, 37P05

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2017
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