TORIC SURFACES OVER AN ARBITRARY FIELD FEILD

摘要

We study tonic varieties over an arbitrary field with an emphasis on tonic surfaces in the Merkurjev-Panin motivic category of "K-motives". We explore the decomposition of certain toric varieties as K-motives into products of central simple algebras, the geometric and topological information encoded in these central simple algebras, and the relationship between the decomposition of the K-motives and the semiorthogonal decomposition of the derived categories. We obtain the information mentioned above for toric surfaces by explicitly classifying all minimal smooth projective toric surfaces using toric geometry.