Vol. 296, No. 2, 2018

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Toric surfaces over an arbitrary field

Fei Xie

Vol. 296 (2018), No. 2, 481–507

We study toric varieties over an arbitrary field with an emphasis on toric 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.

toric variety, motivic category, separable algebra, exceptional collection
Mathematical Subject Classification 2010
Primary: 14J20, 14L30, 14M25
Secondary: 11E72, 16E35, 16H05
Received: 5 May 2017
Revised: 27 November 2017
Accepted: 17 January 2018
Published: 16 July 2018
Fei Xie
Fakultät für Mathematik
Universität Bielefeld