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Mixed Weil cohomologies

- Denis-Charles Cisinski, F. Déglise
- Mathematics
- 20 December 2007

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:… Expand

Around the Gysin triangle I

- F. Déglise
- Mathematics
- 15 April 2008

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… Expand

THE RIGID SYNTOMIC RING SPECTRUM

- F. Déglise, N. Mazzari
- MathematicsJournal of the Institute of Mathematics of…
- 21 November 2012

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… Expand

Orientable homotopy modules

- F. Déglise
- Mathematics
- 23 May 2010

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… Expand

Orientation theory in arithmetic geometry

- F. Déglise
- Mathematics
- 17 November 2011

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… Expand

Around the Gysin triangle II

- F. Déglise
- Mathematics
- 10 December 2007

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… Expand

Construction of Fibred Categories

- Denis-Charles Cisinski, F. Déglise
- MathematicsSpringer Monographs in Mathematics
- 2019

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… Expand

Fibred Categories and the Six Functors Formalism

- Denis-Charles Cisinski, F. Déglise
- MathematicsSpringer Monographs in Mathematics
- 2019

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… Expand

Beilinson Motives and Algebraic K-Theory

- Denis-Charles Cisinski, F. Déglise
- MathematicsSpringer Monographs in Mathematics
- 2019

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.… Expand

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