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Triangulated Categories of Mixed Motives

- Denis-Charles Cisinski, F. D'eglise
- MathematicsSpringer Monographs in Mathematics
- 10 December 2009

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,… Expand

Local and stable homological algebra in Grothendieck abelian categories

- Denis-Charles Cisinski, F. D'eglise
- Mathematics
- 19 December 2007

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… Expand

Étale motives

- Denis-Charles Cisinski, F. D'eglise
- MathematicsCompositio Mathematica
- 23 May 2013

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… Expand

Integral mixed motives in equal characteristic

- Denis-Charles Cisinski, F. D'eglise
- Mathematics
- 23 October 2014

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… Expand

MW-motivic complexes

- F. D'eglise, J. Fasel
- Mathematics
- 21 August 2017

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… Expand

The Milnor-Witt motivic ring spectrum and its associated theories

- F. D'eglise, J. Fasel
- Mathematics
- 21 August 2017

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… Expand

On $p$-adic absolute Hodge cohomology and syntomic coefficients, I

- F. D'eglise, Wiesława Nizioł
- Mathematics
- 11 August 2015

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… Expand

Fundamental classes in motivic homotopy theory

- F. D'eglise, F. Jin, Adeel A. Khan
- Mathematics
- 15 May 2018

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… Expand

Modules homotopiques (Homotopy modules)

- F. D'eglise
- Mathematics
- 30 April 2009

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

- F. D'eglise, M. Bondarko
- Mathematics
- 18 December 2015

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… Expand

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