A tropical Hilbert-Chow morphism

Tropical geometry is often regarded recording the cycle of a variety.  For example, the cohomology class of a subvariety of a toric
variety can be recovered from its tropicalization.  In the recent preprint arXiv.1308.0042 Jeff and Noah Giansiracusa introduced a
notion of scheme structure for tropical varieties.  In the affine case this is a congruence on the tropical semiring.  They show that the
tropical variety as a set is determined by these tropical scheme structure.  I will outline how to also recover the tropical cycle from
this information.  This is joint work with Felipe Rincon.