We construct and study a triangulated category of motives with modulus MDM gm eff over a
field k that extends Voevodsky's category DM gm eff in such a way as to encompass …

Let k be a field of characteristic zero with a fixed embedding W k,! C into the field of complex
numbers. Given a k-variety X, we use the triangulated category of étale motives with rational …

We define a notion of mixed Hodge structure with modulus that generalizes the classical
notion of mixed Hodge structure introduced by Deligne and the level one Hodge structures …

One of the most important results in the theory of motives, as developed by Voevodsky in
[18], is the comparison isomorphism between motivic cohomology groups and higher Chow …

For every noetherian smooth and separated scheme over an algebraically closed field, we
define its derived Albanese in Voevodsky's triangulated category of effective Nisnevich …