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|Named Person:||Alexandre Grothendieck|
|All Authors / Contributors:||
Joseph Ayoub; Fabien Morel; Université Paris Diderot - Paris 7,
|Description:||1 v. (VII-412 p.) ; 30 cm.|
|Responsibility:||Joseph Ayoub ; sous la direction de Fabien Morel.|
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 semi-stable 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.