Speaker: Fei Xie, (UCLA)

Toric varieties over an arbitrary field

Abstract: We study toric varieties over an arbitrary field by studying split toric varieties with Galois actions. Under certain conditions, we can associate a toric variety with a separable algebra in the Merkurjev-Panin motivic category (or K-correspondences). These separable algebras provide geometric information of the corresponding varieties and compute their Algebraic K-groups. We will construct the associated separable algebras for all smooth projective toric surfaces and toric varieties satisfying certain conditions in general. In particular, we will discuss for surfaces the relation between the algebra and the geometry.