  This is my habilitation thesis. As the tradition wants, I tried to give an
introduction of my field of research. I post it on the ArXiv with the hope it
can be useful to young researchers looking for a short and friendly text on
cohomologies of algebraic varieties, periods, algebraic cycles and motives. I
might one day find the energy to expand these notes and maybe translate them in
English. In the meantime, please feel free to ask questions.
  The first sections of this text propose an introduction to the theory, I
tried to present points of view and examples which are not always stressed in
the literature. A leitmotif of the thesis is the difference between phenomena
in characteristic zero and those in positive characteristic.
  The main results are: the standard conjecture of Hodge type for abelian
foufolds; the construction of a class of $p$-adic periods controlled by motivic
Galois groups and for which it is possible to formulate a $p$-adic analog of
the Grothendieck period conjecture; the standard conjecture of Lefschetz type
for the Laza--Sacc\`a--Voisin varieties and the Chow-K\"unneth conjecture for
commutative group schemes. The techniques are based on $p$-adic Hodge theory,
representation theory, perverse sheaves and motivic complexes \`a la Voevodsky.
