Valuations of Weierstrass invariants #
This file records how additive valuations of Weierstrass-curve invariants behave under admissible changes of variables.
Main results #
WeierstrassCurve.ord_Δ_smul: a change of variables subtracts twelve times the order of its scaling parameter from the order of the discriminant.
theorem
WeierstrassCurve.ord_Δ_smul
{K : Type u_1}
[Field K]
(w : Valuation K (WithZero (Multiplicative ℤ)))
(C : VariableChange K)
(W : WeierstrassCurve K)
[W.IsElliptic]
:
A change of variables subtracts twelve times the order of its scaling parameter from the
order of the discriminant. This is a statement about an arbitrary ℤᵐ⁰-valued valuation of
K; the discrete valuation of a local minimal model plays no role.