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fix
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fix
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kim-em committed Oct 3, 2024
1 parent 38c4ed7 commit aa73786
Showing 1 changed file with 5 additions and 4 deletions.
9 changes: 5 additions & 4 deletions Mathlib/AlgebraicGeometry/Modules/Tilde.lean
Original file line number Diff line number Diff line change
Expand Up @@ -187,10 +187,11 @@ lemma smul_section_apply (r : R) (U : Opens (PrimeSpectrum.Top R))
lemma smul_stalk_no_nonzero_divisor {x : PrimeSpectrum R}
(r : x.asIdeal.primeCompl) (st : (tildeInModuleCat M).stalk x) (hst : r.1 • st = 0) :
st = 0 := by
refine Limits.Concrete.colimit_no_zero_smul_divisor (hx := hst)
⟨op ⟨PrimeSpectrum.basicOpen r.1, r.2⟩, fun U i s hs ↦ Subtype.eq <| funext fun pt ↦ ?_⟩
exact LocalizedModule.eq_zero_of_smul_eq_zero (hx := congr_fun (Subtype.ext_iff.1 hs) pt) <|
i.unop pt |>.2
refine Limits.Concrete.colimit_no_zero_smul_divisor
_ _ _ ⟨op ⟨PrimeSpectrum.basicOpen r.1, r.2⟩, fun U i s hs ↦ Subtype.eq <| funext fun pt ↦ ?_⟩
_ hst
apply LocalizedModule.eq_zero_of_smul_eq_zero _ (i.unop pt).2 _
(congr_fun (Subtype.ext_iff.1 hs) pt)

/--
If `U` is an open subset of `Spec R`, this is the morphism of `R`-modules from `M` to
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