Intersection Pairing for Arithmetic Cycles with Degenerate Green Currents
نویسنده
چکیده
As we indicated in our paper [10], the standard arithmetic Chow groups introduced by Gillet-Soulé [4] are rather restricted to consider arithmetic analogues of geometric problems. In this note, we would like to propose a suitable extension of the arithmetic Chow group of codimension one, in which the Hodge index theorem still holds as in papers [2], [8] and [15]. Let X → Spec(Z) be a regular arithmetic variety with d = dimXQ. As we defined in [10], ĈH p D(X) is a group, consisting of pairs (Z, g) with cycles Z of codimension p on X and currents g of type (p−1, p−1) onX(C), modulo arithmetical rational equivalence. It seems to
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Hodge Index Theorem for Arithmetic Divisors with Degenerate Green Functions
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