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