On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties

Jörg Wildeshaus (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

Applying the main results of our previous work 0806.3380, we construct a Hecke-equivariant Chow motive whose realizations equal interior cohomology of Hilbert-Blumenthal varieties with non-constant coefficients.

Mots clés: Artin-Tate motives; weight structures; relative motives; boundary motive; interior motive; Hilbert-Blumenthal varieties

Domaines: Géométrie algébrique [math.AG]; K-théorie et homologie [math.KT]

Jörg Wildeshaus. On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties. International Mathematics Research Notices, 2012, 2012 (10), pp.2321-2355. ⟨10.1093/imrn/rnr109⟩. ⟨hal-00401296⟩