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Triangulated Categories of Mixed Motives
This book discusses the construction of triangulated categories of mixed motives over a noetherian scheme of finite dimension, extending Voevodsky's definition of motives over a field. In particular,
Local and stable homological algebra in Grothendieck abelian categories
We define model category structures on the category of chain complexes over a Grothendieck abelian category depending on the choice of a generating family, and we study their behaviour with respect
Étale motives
We define a theory of étale motives over a noetherian scheme. This provides a system of categories of complexes of motivic sheaves with integral coefficients which is closed under the six operations
Integral mixed motives in equal characteristic
For noetherian schemes of finite dimension over a field of characteristic exponent $p$, we study the triangulated categories of $\mathbf{Z}[1/p]$-linear mixed motives obtained from cdh-sheaves with
MW-motivic complexes
The aim of this work is to develop a theory parallel to that of motivic complexes based on cycles and correspondences with coefficients in quadratic forms. This framework is closer to the point of
The Milnor-Witt motivic ring spectrum and its associated theories
We build a ring spectrum representing Milnor-Witt motivic cohomology, as well as its \'etale local version and show how to deduce out of it three other theories: Borel-Moore homology, cohomology with
On $p$-adic absolute Hodge cohomology and syntomic coefficients, I
We interpret syntomic cohomology of Nekov\'a\v{r}-Nizio{\l} as a $p$-adic absolute Hodge cohomology. This is analogous to the interpretation of Deligne-Beilinson cohomology as an absolute Hodge
Fundamental classes in motivic homotopy theory
We develop the theory of fundamental classes in the setting of motivic homotopy theory. Using this we construct, for any motivic spectrum, an associated bivariant theory in the sense of
Modules homotopiques (Homotopy modules)
The proof of the coincidence of the Gysin morphism in motivic cohomology and the usual pushout on Chow groups has been improved (see Lemma 3.3 and Proposition 3.11)
Dimensional homotopy t-structure in motivic homotopy theory
The aim of this work is to construct certain homotopy t-structures on various categories of motivic homotopy theory, extending works of Voevodsky, Morel, D\'eglise and Ayoub. We prove these