Morel, Fabien
Overview
Works:  11 works in 62 publications in 3 languages and 1,461 library holdings 

Roles:  Author, dgs, Thesis advisor 
Classifications:  QA564, 514.72 
Publication Timeline
.
Most widely held works by
Fabien Morel
Algebraic cobordism by
Marc Levine(
Book
)
18 editions published between 2006 and 2010 in English and held by 194 WorldCat member libraries worldwide
Following Quillen's approach to complex cobordism, this book introduces the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. It also contains some examples of computations and applications
18 editions published between 2006 and 2010 in English and held by 194 WorldCat member libraries worldwide
Following Quillen's approach to complex cobordism, this book introduces the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. It also contains some examples of computations and applications
Théorie homotopique des schémas by
Fabien Morel(
Book
)
10 editions published in 1999 in French and Italian and held by 170 WorldCat member libraries worldwide
10 editions published in 1999 in French and Italian and held by 170 WorldCat member libraries worldwide
A¹algebraic topology over a field by
Fabien Morel(
Book
)
20 editions published in 2012 in English and held by 156 WorldCat member libraries worldwide
This text deals with A1homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1homotopy sheaves, A1homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties
20 editions published in 2012 in English and held by 156 WorldCat member libraries worldwide
This text deals with A1homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1homotopy sheaves, A1homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties
Homotopy theory of schemes by
Fabien Morel(
Book
)
5 editions published in 2006 in English and held by 149 WorldCat member libraries worldwide
5 editions published in 2006 in English and held by 149 WorldCat member libraries worldwide
Invertible objects in motivic homotopy theory by Tom Bachmann(
)
1 edition published in 2016 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2016 in English and held by 16 WorldCat member libraries worldwide
Noise sensitivity of Boolean functions and applications to percolation. A 1homotopy theory of schemes / by Fabien Morel ;
Vladimir Voevodsky [u.a.] by
Itai Benjamini(
Book
)
1 edition published in 2001 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 5 WorldCat member libraries worldwide
Caractérisation des foncteurs homotopiques covariants représentables par un espace pointé connexe et applications by
Fabien Morel(
Book
)
2 editions published in 1991 in French and held by 4 WorldCat member libraries worldwide
On démontre un résultat dual du théorème de représentabilité de E.H. Brown et l'on décrit quelques applications. La première partie du mémoire contient une caractérisation des foncteurs homotopique covariants représentables par un espace pointé connexe ; on en donne comme application immédiate la construction plus de D. Quillen. La seconde partie décrit une démonstration d'un théorème de J. Lannes qui s'inspire de la technique de la première partie. La troisième partie de ce mémoire en est le coeur : c'est la reproducton d'un article rédigé en collaboration avec P. Goerss et J. Lannes sur la représentabilité de l'homologie modulo P
2 editions published in 1991 in French and held by 4 WorldCat member libraries worldwide
On démontre un résultat dual du théorème de représentabilité de E.H. Brown et l'on décrit quelques applications. La première partie du mémoire contient une caractérisation des foncteurs homotopique covariants représentables par un espace pointé connexe ; on en donne comme application immédiate la construction plus de D. Quillen. La seconde partie décrit une démonstration d'un théorème de J. Lannes qui s'inspire de la technique de la première partie. La troisième partie de ce mémoire en est le coeur : c'est la reproducton d'un article rédigé en collaboration avec P. Goerss et J. Lannes sur la représentabilité de l'homologie modulo P
Modules homotopiques avec transferts et motifs génériques by
Frédéric Déglise(
Book
)
1 edition published in 2002 in French and held by 2 WorldCat member libraries worldwide
1 edition published in 2002 in French and held by 2 WorldCat member libraries worldwide
A1homotopy theory of schemes by
Fabien Morel(
Book
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
A¹^algebraic topology by
Fabien Morel(
)
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique by
Joseph Ayoub(
Book
)
1 edition published in 2006 in French and held by 1 WorldCat member library worldwide
The goal of the thesis is to do for motives what was done for etale cohomology in SGA 4 and SGA 7. Unfortunately, this Project is extremely difficult and put of reach of actual techniques. This is due to the fact that the motives we are using lives in a trianqulated category rather than an abelian one. Nevertheless, we were able to obtain the motivic analogue of many results of SGA 4 and SGA 7. We have constructed the remaininq operations. We proved the base change theorems, the constructability and cohomological dimension theorems, We established Verdier duality. We computed the nearby cycles in the semistable reduction situation and proved the unipotence of the monodrorny operator. What we didn't do: Artin theorern on the cohomological dimension of an affine scheme the global theory of vanishing cycles, etc
1 edition published in 2006 in French and held by 1 WorldCat member library worldwide
The goal of the thesis is to do for motives what was done for etale cohomology in SGA 4 and SGA 7. Unfortunately, this Project is extremely difficult and put of reach of actual techniques. This is due to the fact that the motives we are using lives in a trianqulated category rather than an abelian one. Nevertheless, we were able to obtain the motivic analogue of many results of SGA 4 and SGA 7. We have constructed the remaininq operations. We proved the base change theorems, the constructability and cohomological dimension theorems, We established Verdier duality. We computed the nearby cycles in the semistable reduction situation and proved the unipotence of the monodrorny operator. What we didn't do: Artin theorern on the cohomological dimension of an affine scheme the global theory of vanishing cycles, etc
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Audience Level
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Related Identities
 Levine, Marc 1952 Author
 Bachmann, Tom Author
 Lewis, James Dominic (1953 ...).
 Université Paris Diderot  Paris 7 Degree grantor
 Voevodsky, Vladimir
 Kalai, Gil
 Schramm, Oded
 Benjamini, Itai Author
 Lannes, Jean
 Déglise, Frédéric (1975 ...). Author
Useful Links
Alternative Names
Fabien Morel Frans wiskundige
Fabien Morel fransk matematikar
Fabien Morel fransk matematiker
Fabien Morel französischer Mathematiker
Fabien Morel French mathematician
Fabien Morel matemático francés
Fabien Morel mathématicien français
Morel, F.
Morel, F. 1965
Morel, F. (Fabien)
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