Exemples de classification du champ des faisceaux pervers

Abstract

In this thesis we show how to use stack theory to glue description of the category of perverse sheaves P(X,S) on a stratified space (X,S). Hence we give new description of P(X,S) when X is locally C^n stratified by the stratification S given by the normal crossing. First we give a characterization of the 2-category of a stack on a stratified space. Thank to this and to a description in term of quiver's representation of the category P(C^n,S) due to Galligo, Granger, Maisonobe, we define a stack on C^n constructible relatively to S, equivalent to the stack Perv(C,S) of perverse sheaves on C^n relatively to S. As a stack can be define on an open covering and as toric varieties and C^2 stratified by a generic hyperplanes arrangement are locally isomorphic to (C^n,S) we can define a stack CC on these spaces equivalent to the stack PervX. Then a study of the global sections of CC gives a category of quivers representations equivalent to the category P(X,S').