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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.
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참고문헌 (41)
참고문헌 신청
M. Artin / 1969 / Etale homotopy / Lecture Notes in Mathematics 100
M. Atiyah / 1961 / Vector bundles and homogeneous spaces / Proc. Sympos. Pure Math. 3:7~38
M. Atiyah / 1962 / The Riemann-Roch theorem for analytic embeddings / Topology 1:151~166
A. A. Beilinson / 1978 / Coherent sheaves on Pn and problems of linear algebra / Funct. Anal. Appl 12(3):66~67
M. Bernardara / 2015 / Relations between the Chow motive and the noncommutative motive of a smooth projective variety / J. Pure Appl. Algebra 219(11):5068~5077
M. Atiyah / 1961 / Vector bundles and homogeneous spaces / Proc. Sympos. Pure Math. 3:7~38
M. Atiyah / 1962 / The Riemann-Roch theorem for analytic embeddings / Topology 1:151~166
A. A. Beilinson / 1978 / Coherent sheaves on Pn and problems of linear algebra / Funct. Anal. Appl 12(3):66~67
M. Bernardara / 2015 / Relations between the Chow motive and the noncommutative motive of a smooth projective variety / J. Pure Appl. Algebra 219(11):5068~5077
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