Resumen de Unramified elements in cycle modules

Alexander S. Merkurjev

• Let X be an algebraic variety over a field F. We study the functor taking a cycle module M over F to the group of unramified elements M(F(X))nr of M(F(X)). We prove that this functor is represented by a cycle module. The existence of pull-back maps on M(F(X))nr for rational maps (under a mild condition) is established. An application to the R-equivalence on classifying varieties of algebraic groups is given.