Equivariant non-archimedean Arakelov theory of toric varieties

TL;DR

This paper develops an equivariant non-archimedean Arakelov theory for toric varieties, providing combinatorial descriptions of Green currents and arithmetic Chow groups, extending previous non-equivariant frameworks.

Contribution

It introduces an equivariant framework for non-archimedean Arakelov theory on toric varieties, with combinatorial characterizations of key objects.

Findings

Defined equivariant non-archimedean differential forms and currents

Provided combinatorial characterizations of Green currents

Described arithmetic Chow groups in the equivariant setting

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.