摘要 : Let X be a curve over a field k with a rational point e. We define a canonical cycle Δ_e ∈ Z~2(X~3)_(hom). Suppose that fc is a number field and that X has semi-stable reduction over the integers of fc with fiber components non-si... 展开 Let X be a curve over a field k with a rational point e. We define a canonical cycle Δ_e ∈ Z~2(X~3)_(hom). Suppose that fc is a number field and that X has semi-stable reduction over the integers of fc with fiber components non-singular. We construct a regular model of X~3 and show that the height pairing < τ* (Δe), τ′* (Δe) > is well defined where τ and τ′ are correspondences. The paper ends with a brief discussion of heights and L-functions in the case that X is a modular curve. 收起