Relative cycle

In algebraic geometry, a relative cycle is a type of algebraic cycle on a scheme. In particular, let ${\displaystyle X}$ be a scheme of finite type over a Noetherian scheme ${\displaystyle S}$, so that ${\displaystyle X\rightarrow S}$. Then a relative cycle is a cycle on ${\displaystyle X}$ which lies over the generic points of ${\displaystyle S}$, such that the cycle has a well-defined specialization to any fiber of the projection ${\displaystyle X\rightarrow S}$.(Voevodsky & Suslin 2000)

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.