The coherent sheaves defined on a separated noetherian scheme X reflect the underlying
geometry, and they play a central role in modern algebraic geometry. Recent results have …

We show that the category of mixed Hodge complexes admits a Cartan-Eilenberg structure,
a notion introduced by Guillén-Navarro-Pascual-Roig leading to a good calculation of the …

In this paper, we introduce a cofibrant simplicial category that we call the free homotopy
coherent adjunction and characterise its n-arrows using a graphical calculus that we …

We show how derived categories build bridges across the current mathematical mainstream,
linking geometric and algebraic, commutative and noncommutative, local and global banks …

We establish a connection between differential graded and simplicial categories by
constructing a three-step zig-zag of Quillen adjunctions relating the homotopy theories of the …

Given an appropriate diagram of left Quillen functors between model categories, one can
define a notion of homotopy fiber product, but one might ask if it is really the correct one …

For a suitable choice of the cube category, we construct a Grothendieck topology on it such
that sheaves with respect to this topology are exactly simplicial sets (thus establishing …

We give scheme-theoretic descriptions of the category of fibre functors on the categories of
sheaves associated to the Zariski, Nisnevich, étale, rh, cdh, ldh, eh, qfh, and h topologies on …

The paper contains general results on the uniqueness of a DG enhancement for triangulated
categories. As a consequence we obtain such uniqueness for the unbounded derived …

We prove in this paper that for a quasi-compact and semi-separated (nonnecessarily
noetherian) scheme X, the derived category of quasi-coherent sheaves over X, D (Aqc (X)) …