Let $ X $ be a smooth scheme, $ Z $ a smooth closed subscheme, and $ U $ the open
complement. Given any localizing and $\mathbb {A}^ 1$-homotopy invariant of dg …

We introduce a notion of fine Tannakian infinity‐categories and prove Tannakian
characterization resuls for symmetric monoidal stable infinity‐categories over a field of …

The goal of this series of papers is to give a new non-commutative approach to problems
about the density of reductions such as the conjecture of Joshi-Rajan, and the …

Waldhausen's K-theory of the sphere spectrum (closely related to the algebraic K-theory of
the integers) is naturally augmented as an S 0-algebra, and so has a Koszul dual. Classic …

In this paper we construct new derived invariants with integral coefficients using the theory of
motifs, and give several applications. Specifically, we obtain the following results: For …

In this paper, we construct four different theories of integration, two that are for Voevodsky
motives, one for mixed $\ell $-adic sheaves, and a fourth theory of integration for rational …

In this article, we propose noncommutative versions of Tate conjecture and Hodge
conjecture. If we consider these conjectures for a dg-category of perfect complexes over a …

This article is the sequel to (Marcolli and Tabuada in Sel Math 20 (1): 315–358, 2014). We
start by developing a theory of noncommutative (= NC) mixed motives with coefficients in …

Let Q-> B be a quadric fibration and T-> B a family of sextic du Val del Pezzo surfaces.
Making use of the recent theory of noncommutative mixed motives, we establish a precise …

Kimura-finiteness of quadric fibrations over smooth curves Page 1 CR Acad. Sci. Paris, Ser. I
355 (2017) 628–632 Contents lists available at ScienceDirect CR Acad. Sci. Paris, Ser. I …