Equivariant non-archimedean Arakelov theory of toric varieties

Abstract

We develop an equivariant version of the non-archimedean Arakelov theory of [BGS95] in the case of toric varieties. We define the equivariant analogues of the non-archimedean differential forms and currents appearing in \emph{loc.~cit.} and relate them to piecewise polynomial functions on the polyhedral complexes defining the toric models. In particular, we give combinatorial characterizations of the Green currents associated to equivariant cycles and combinatorial descriptions of the arithmetic Chow groups.