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Abstract
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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.
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Keywords
toric variety, motivic category, separable algebra,
exceptional collection
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Mathematical Subject Classification 2010
Primary: 14J20, 14L30, 14M25
Secondary: 11E72, 16E35, 16H05
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Milestones
Received: 5 May 2017
Revised: 27 November 2017
Accepted: 17 January 2018
Published: 16 July 2018
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