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Mixed Weil cohomologies
Abstract We define, for a regular scheme S and a given field of characteristic zero K, the notion of K-linear mixed Weil cohomology on smooth S-schemes by a simple set of properties, mainly:
Around the Gysin triangle I
We study the construction and properties of the Gysin triangle in an axiomatic framework which covers triangulated mixed motives and MGl-modules over an arbitrary base S. This allows to define the
The aim of this paper is to show that rigid syntomic cohomology – defined by Besser – is representable by a rational ring spectrum in the motivic homotopical sense. In fact, extending previous
Orientable homotopy modules
We prove a conjecture of Morel identifying Voevodsky’s homotopy invariant sheaves with transfers with spectra in the stable homotopy category which are concentrated in degree zero for the homotopy
Orientation theory in arithmetic geometry
This work is devoted to study orientation theory in arithmetic geometric within the motivic homotopy theory of Morel and Voevodsky. The main tool is a formulation of the absolute purity property for
Around the Gysin triangle II
The notions of orientation and duality are well understood in algebraic topology in the framework of the stable homotopy category. In this work, we follow these lines in algebraic geometry, in the
Construction of Fibred Categories
In Section 5, we introduce methods from classical homological algebra (i.e. using mostly the language of derived categories of abelian categories and their Verdier quotients) to construct the main
Fibred Categories and the Six Functors Formalism
In Section 1, we introduce the basic language used in this book, the so-called premotivic categories and their functoriality. This is an extension of the classical notion of fibered categories. They
Beilinson Motives and Algebraic K-Theory
Section 12 is a recollection on the basic results of stable homotopy theory of schemes, after Morel and Voevodsky. In particular, we recall the theory of orientations in a motivic cohomology theory.