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

Some arithmetic and geometric aspects of algebraic cycles and motives