On a motivic interpretation of primitive, variable and fixed cohomology

C. Peters (Corresponding author)

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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.

Original languageEnglish
Pages (from-to)402-408
Number of pages7
JournalMathematische Nachrichten
Issue number2
Early online date4 Oct 2018
Publication statusPublished - 1 Feb 2019


  • algebraic cycles
  • finite-dimensional motives
  • primitive
  • vanishing and fixed cohomology

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