On a motivic interpretation of primitive, variable and fixed cohomology

Chris Peters

Mathematische Nachrichten, 2019, vol. 292, issue 2, 402-408

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.

Date: 2019
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