Around Rationality of Algebraic Cycles by

iAbstract Let F be a field and X, Y some F-varieties. In this dissertation, we are interested in knowing if the class y ∈ CH(YF (X)) of an algebraic cycle defined over the function field F (X) is actually defined over the base field, i.e belongs to the image of the pull-back homomorphism CH(Y) → CH(YF (X)). We study this issue in different contexts, the variety X varying among classes of varieties such as quadrics or projective homogeneous varieties