Math @ Duke

Publications [#345774] of Joseph D Rabinoff
Papers Published
 Rabinoff, J, Tropical analytic geometry, Newton polygons, and tropical intersections,
Advances in Mathematics, vol. 229 no. 6
(April, 2012),
pp. 31923255 [doi]
(last updated on 2021/08/04)
Abstract: In this paper we use the connections between tropical algebraic geometry and rigidanalytic geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in several variables: if f 1, ..., f n are n convergent power series in n variables with coefficients in a nonArchimedean field K, we give a formula for the valuations and multiplicities of the common zeros of f 1, ..., f n. We use rigidanalytic methods to show that stable complete intersections of tropical hypersurfaces compute algebraic multiplicities even when the intersection is not tropically proper. These results are naturally formulated and proved using the theory of tropicalizations of rigidanalytic spaces, as introduced by Einsiedler, Kapranov, and Lind (2006) [14] and Gubler (2007) [20]. We have written this paper to be as readable as possible both to tropical and arithmetic geometers. © 2012 Elsevier Inc..


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