Non-archimedean curves, abelian varieties, and faithful tropicalization

Farbod Shokrieh, Cornell

The skeleton of a Berkovich analytic space is a subspace onto which the whole space deformation retracts. For an abelian variety, the skeleton is a real torus with an “integral structure”. I will discuss “faithful tropicalization” of abelian varieties in terms of non-archimedean and tropical theta functions. The solution relies on interesting combinatorial facts about lattices, matroids, and Voronoi decompositions. This talk is based on joint work with Tyler Foster, Joe Rabinoff, and Alejandro Soto. I will not assume any prior knowledge about non-archimedean geometry or tropicalization.

Tuesday, November 10th, at 4:00pm in HBH 227

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