Relative cycle

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

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.