Morel, Fabien
Overview
Works:  11 works in 59 publications in 3 languages and 1,416 library holdings 

Roles:  Author 
Classifications:  QA564, 514.72 
Publication Timeline
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Most widely held works by
Fabien Morel
Homotopy theory of schemes by
Fabien Morel(
Book
)
14 editions published between 1999 and 2006 in French and English and held by 318 WorldCat member libraries worldwide
14 editions published between 1999 and 2006 in French and English and held by 318 WorldCat member libraries worldwide
Algebraic cobordism by
Marc Levine(
Book
)
16 editions published between 2007 and 2010 in English and held by 190 WorldCat member libraries worldwide
Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications
16 editions published between 2007 and 2010 in English and held by 190 WorldCat member libraries worldwide
Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications
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
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
Carte géologique du Djebel Belkfif [Algérie], 1:20 000(
)
1 edition published in 1957 in French and held by 1 WorldCat member library worldwide
1 edition published in 1957 in French 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
Theorie hoomootopique des schemas by
Fabien Morel(
Book
)
1 edition published in 1999 in Italian and held by 1 WorldCat member library worldwide
1 edition published in 1999 in Italian and held by 1 WorldCat member library 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
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