Algebraic and Tropical Intersection Numbers
نویسندگان
چکیده
We prove that if X,X are closed subschemes of a torus T over a non-Archimedean field K, of complementary codimension and with finite intersection, then the stable tropical intersection along a (possibly positive-dimensional, possibly unbounded) connected componentC of Trop(X)∩Trop(X) lifts to algebraic intersection points, with multiplicities. This theorem requires potentially passing to a suitable toric varietyX(∆) and its associated Kajiwara-Payne extended tropicalizationNR(∆). The proof involves a result on continuity of intersection numbers in the context of non-Archimedean analytic spaces.
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