baseChange — Mathlib

English

The base change map between affine Weierstrass coordinates is a canonical group homomorphism induced by a change of base ring.

Русский

Базовое изменение координат аффинной кривой Вейерштрасса является каноническим гомоморфизмом группы, индуцируемым изменением базы кольца.

LaTeX

$$$\text{baseChange}$ is a group homomorphism from $W'⟮F⟯$ to $W'⟮K⟯$ induced by the canonical map $F\to K$$$

Lean4

/-- The group homomorphism from `W⟮F⟯` to `W⟮K⟯` induced by the base change from `F` to `K`, where
`W` is defined over a subring of a ring `S`, and `F` and `K` are field extensions of `S`. -/
noncomputable abbrev baseChange [Algebra F K] [IsScalarTower R F K] : W'⟮F⟯ →+ W'⟮K⟯ :=
  map <| Algebra.ofId F K

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