Integral Chow motives of threefolds with $K$-motives of unit type

Sergey Gorchinskiy

doi:10.4134/BKMS.b160759

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(5): 1827-1849

Online first article July 26, 2017 Printed September 30, 2017

https://doi.org/10.4134/BKMS.b160759

Integral Chow motives of threefolds with $K$-motives of unit type

Sergey Gorchinskiy

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract

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Abstract

We prove that if a smooth projective algebraic variety of dimension less or equal to three has a unit type integral $K$-motive, then its integral Chow motive is of Lefschetz type. As a consequence, the integral Chow motive is of Lefschetz type for a smooth projective variety of dimension less or equal to three that admits a full exceptional collection.

Keywords: $K$-motives, Chow motives, exceptional collections

MSC numbers: 14C15, 14C35