62.1 Introduction
A foundational reference is [SV].
In this chapter we only define what are called the universally integral relative cycles in [SV]. This choice makes the theory somewhat simpler to develop than in the original, but of course we also lose something.
Fix a morphism X \to S of finite type between Noetherian schemes. A family \alpha of r-cycles on fibres of X/S is simply a collection \alpha = (\alpha _ s)_{s \in S} where \alpha _ s \in Z_ r(X_ s). It is immediately clear how to base change g^*\alpha of \alpha along any morphism g : S' \to S. Then we say \alpha is a relative r-cycle on X/S if \alpha is compatible with specializations, i.e., for any morphism g : S' \to S where S' is the spectrum of a discrete valuation ring, we require the generic fibre of g^*\alpha to specialize to the closed fibre of g^*\alpha . See Section 62.6.
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