  The aim of this thesis is to study the dg categories of singularities
Sing(X,s) of pairs (X,s), where X is a scheme and s is a global section of some
vector bundle over X. Sing(X,s) is defined as the kernel of the dg functor from
Sing(X_0) to Sing(X) induced by the pushforward along the inclusion of the
(derived) zero locus X_0 of s in X.
  In the first part, we restrict ourselves to the case where the vector bundle
is trivial. We prove a structure theorem for Sing(X,s) when X=Spec(B) is
affine. Roughly, it tells us that every object in Sing(X,s) is represented by a
complex of B-modules concentrated in n+1 consecutive degrees (if s \in B^n). By
specializing to the case n=1, we generalize Orlov's theorem, which identifies
Sing(X,s) with the dg category of matrix factorizations MF(X,s), to the case
where s \in O_X(X) is not flat.
  In the second part, we study the l-adic cohomology of Sing(X,s) (as defined
by A.~Blanc - M.~Robalo - B.~To\"en and G.~Vezzosi) when s is a global section
of a line bundle. In order to do so, we introduce the l-adic sheaf of
monodromy-invariant vanishing cycles. Using a theorem of D.~Orlov generalized
by J.~Burke and M.~Walker, we compute the l-adic realization of
Sing(Spec(B),(f_1,..,f_n)) for (f_1,..,f_n) \in B^n.
  In the last chapter, we introduce the l-adic sheaves of iterated vanishing
cycles of a scheme over a discrete valuation ring of rank 2. We relate one of
these l-adic sheaves to the l-adic realization of the dg category of
singularities of the fiber over a closed subscheme of the base.
