Common use of Proposition 1 Clause in Contracts

Proposition 1. The pullback of P by (▇▇, jv,−1) : C ×S J → J ×S J∨ together with its rigidifications at b and 0, is equal to Luniv. Let d be in Z≥0. The morphism : C(d) → J∨ = Pic0 Σ: C(d) → J, sending, for every S-scheme T, each point D in C(d)(T ) to the class of OCT (D − db) twisted by the pullback from T that makes it rigidified at b, followed by jv,−1 : J → J∨. Summarised in a diagram, with M := (id × jv,−1)vP: Luniv P M (1.6.3.3) i˜d×Σ Nd jb×j𝗁,−1 id×j𝗁,−1 id×Σ ( ) C ×S J J ×S J∨ J ×S J J ×S C d .