Constructible sheaves on toric varieties

Abstract

This paper gives an explicit computation of the category of constructible sheaves on a toric variety (with respect to the stratification by torus orbits). Over the complex numbers, this simplifies a description due to Braden and Lunts. The same computation is carried out for split toric varieties over an arbitrary field, for constructible \'etale sheaves whose restriction to each stratum is locally constant and tamely ramified. This gives the first explicit computation of an \'etale exodromy theorem in positive characteristic for a stratification over a partially ordered set of height greater than 1.