Weierstrass Curve tate Curve base Change
WeierstrassCurve.tateCurve_baseChange
Plain-language statement
The construction of the Tate curve commutes on the nose with any valuative morphism: its coefficients are power series in q with integer coefficients, and the partial sums converge at matching rates on both sides (TateCurve.evalInt_map). The same is true of the uniformisation tateCurveEquiv (a statement we defer, as it needs transport along this e...
Exact Lean statement
theorem WeierstrassCurve.tateCurve_baseChange (q : k) (hq : valuation k q < 1) :
(tateCurve q)⁄l = tateCurve (algebraMap k l q)Formal artifact
Lean source
theorem WeierstrassCurve.tateCurve_baseChange (q : k) (hq : valuation k q < 1) : (tateCurve q)⁄l = tateCurve (algebraMap k l q) := by have hq' : valuation l (algebraMap k l q) < 1 := TateCurve.valuation_algebraMap_lt_one hq have h4 : algebraMap k l (tateA₄ q) = tateA₄ (algebraMap k l q) := by rw [tateA₄_eq_evalInt q hq, tateA₄_eq_evalInt _ hq', TateCurve.evalInt_map q hq] have h6 : algebraMap k l (tateA₆ q) = tateA₆ (algebraMap k l q) := by rw [tateA₆_eq_evalInt q hq, tateA₆_eq_evalInt _ hq', TateCurve.evalInt_map q hq] ext <;> simp [WeierstrassCurve.baseChange, tateCurve, h4, h6]- Project
- Fermat's Last Theorem
- License
- Apache-2.0
- Commit
- 8dd808888295
- Source
- FLT/KnownIn1980s/EllipticCurves/TateCurve.lean:351-358
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