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On a motivic interpretation of primitive, variable and fixed cohomology

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  • Chris Peters

Abstract

If M is a smooth projective variety whose motive is Kimura finite‐dimensional and for which the standard Lefschetz Conjecture B holds, then the motive of M splits off a primitive motive whose cohomology is the primitive cohomology. Under the same hypotheses on M, let X be a smooth complete intersection of ample divisors within M. Then the motive of X is the sum of a variable and a fixed motive inducing the corresponding splitting in cohomology. I also give variants with group actions.

Suggested Citation

  • Chris Peters, 2019. "On a motivic interpretation of primitive, variable and fixed cohomology," Mathematische Nachrichten, Wiley Blackwell, vol. 292(2), pages 402-408, February.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:2:p:402-408
    DOI: 10.1002/mana.201800011
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