Chow motives without projectivity, II

Jörg Wildeshaus (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

The purpose of this article is to provide a simplified construction of the intermediate extension of a Chow motive, provided a condition on absence of weights in the boundary is satisfied. We give a criterion, which guarantees the validity of the condition, and compare our new construction to the theory of the interior motive established earlier. We finish the article with a review of the known applications to the boundary of Shimura varieties.

Mots clés: weight structures; boundary motive; interior motive; motivic intermediate extension; intersection motive

Domaines: Géométrie algébrique [math.AG]

Jörg Wildeshaus. Chow motives without projectivity, II. International Mathematics Research Notices, 2018, 2020 (23), pp.9593-9639. ⟨10.1093/imrn/rny257⟩. ⟨hal-01545527⟩