Relative cycle

In algebraic geometry, a relative cycle is a type of algebraic cycle on a scheme. In particular, let formula_1 be a scheme of finite type over a Noetherian scheme formula_2, so that formula_3. Then a relative cycle is a cycle on formula_1 which lies over the generic points of formula_2, such that the cycle has a well-defined specialization to any fiber of the projection formula_3.
The notion was introduced by Andrei Suslin and Vladimir Voevodsky in 2000; the authors were motivated to overcome some of the deficiencies of sheaves with transfers.