Arithmetic Chow Groups
An arithmetic cycle of codimension p is a pair (Z, g) where Z ∈ Zp(X) is a p-cycle on X and g is a Green current for Z, a higher dimensional generalization of a Green function. The arithmetic Chow group of codimension p is the quotient of this group by the subgroup generated by certain "trivial" cycles.
Read more about this topic: Arakelov Theory
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