On complete intersections in varieties with finite-dimensional motive

R. Laterveer (Corresponding author), J. Nagel, C.A.M. Peters

Research output: Contribution to journalArticleAcademicpeer-review

62 Downloads (Pure)

Abstract

Let X be a complete intersection inside a variety M with finite-dimensional motive and for which the Lefschetz-type conjecture B(M) holds. We show how conditions on the niveau filtration on the homology of X influence directly the niveau on the level of Chow groups. This leads to a generalization of Voisin's result. The latter states that if M has trivial Chow groups and if X has non-trivial variable cohomology parametrized by c-dimensional algebraic cycles, then the cycle class maps A k (X) → H 2k (X) are injective for k<c. We give variants involving group actions, which lead to several new examples with finite-dimensional Chow motives.

Original languageEnglish
Pages (from-to)71-104
Number of pages34
JournalThe Quarterly Journal of Mathematics
Volume70
Issue number1
DOIs
Publication statusPublished - 1 Mar 2019

Keywords

  • math.AG
  • 14C15, 14C25, 14C30

Fingerprint Dive into the research topics of 'On complete intersections in varieties with finite-dimensional motive'. Together they form a unique fingerprint.

  • Cite this