Theorems · Definition · algebraic geometry

WeierstrassCurve.Affine.Point.map

{R : Type r} →
  {S : Type s} →
    {F : Type u} →
      {K : Type v} →
        [inst : CommRing R] →
          [inst_1 : CommRing S] →
            [inst_2 : Field F] →
              [inst_3 : Field K] →
                {W' : WeierstrassCurve.Affine R} →
                  [inst_4 : DecidableEq F] →
                    [inst_5 : DecidableEq K] →
                      [inst_6 : Algebra R S] →
                        [inst_7 : Algebra R F] →
                          [inst_8 : Algebra S F] →
                            [IsScalarTower R S F] →
                              [inst_10 : Algebra R K] →
                                [inst_11 : Algebra S K] →
                                  [IsScalarTower R S K] →
                                    (F →ₐ[S] K) → (W'.baseChange F).Point →+ (W'.baseChange K).Point

The group homomorphism on nonsingular points induced by an algebra homomorphism f : F →ₐ[S] K, where W is defined over a subring of a ring S, and F and K are field extensions of S.

Defined in

Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point

Cited by

6 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingFieldFieldDecidableEqDecidableEqAlgebraAlgebraAlgebraIsScalarTowerAlgebraAlgebraIsScalarTower