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49677ca | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | import OAI.AlgebraicGeometry.CartierSections.FieldTopology
import OAI.AlgebraicGeometry.CartierSections.FieldRetraction
namespace OAI
noncomputable section
open scoped BigOperators NNReal ENNReal
namespace CartierSections
section ClosedChartFieldTopology
universe u
local instance polynomialOrigin_isMaximal_topology {σ k : Type u} [Fintype σ] [Field k] :
(MvPolynomial.idealOfVars σ k).IsMaximal :=
polynomialOrigin_isMaximal
variable {σ k R A K : Type u} [Fintype σ] [Field k] [IsAlgClosed k]
[CommRing R] [CommRing A] [IsLocalRing R] [IsLocalRing A] [IsNoetherianRing A]
[IsDomain A] [Field K] [Algebra A K] [IsFractionRing A K]
[Algebra (MvPolynomial σ k) R] [Algebra (MvPolynomial σ k) A]
[Algebra k A] [IsScalarTower k (MvPolynomial σ k) A]
[Algebra R A] [IsScalarTower (MvPolynomial σ k) R A]
[IsLocalization.AtPrime R (MvPolynomial.idealOfVars σ k)]
[IsLocalHom (algebraMap R A)] [Algebra.FormallyUnramified R A]
[Algebra.EssFiniteType R A] [Algebra.FormallyEtale (MvPolynomial σ k) A]
lemma isCompact_closedChartFieldRetraction_cone
(a : σ → NNReal) (ha : ∀ i, 0 < a i) :
IsCompact ((fun w : σ → NNReal => fun x : K =>
closedChartFieldRetraction (σ := σ) (k := k) (R := R) (A := A) w x) ''
normalizedWeights a) := by
sorry
end ClosedChartFieldTopology
end CartierSections
end
end OAI
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