Keel, Seán2011-03-212017-05-112011-03-212017-05-112009-08http://hdl.handle.net/2152/10604textLet Y be a subvariety of an algebraic torus, Tevelv (24) defined and studied tropical compactifications as certain nice compactifications of Y. We give a criterion for certain compactification to be a schön compactification, and as a corollary, we show that any variety contains an open very affine schön variety. Using toric schemes defined over a discrete valuation ring, we generalize the theory of tropical compactification to the nonconstant coefficient case, i.e. for varieties defined over a discrete valuation ring.electronicengCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.Toric schemesDiscrete valuation ringTropical compactificationsSchön variety