Structure Sheaf on Basic Opens #728
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mzeuner
commented
Mar 1, 2022
| R[1/fg]≡R[1/f][1/g] : R[1/fg]AsCommAlgebra ≡ R[1/f][1/g]AsCommAlgebra | ||
| R[1/fg]≡R[1/f][1/g] = uaCommAlgebra (R[1/fg]AlgCharEquiv _ _ pathtoR[1/fg]) | ||
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| doubleLocCancel : g ∈ᵢ √ ⟨ replicateFinVec 1 f ⟩ → R[1/f][1/g]AsCommAlgebra ≡ R[1/g]AsCommAlgebra |
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Nicer notation for ⟨ replicateFinVec 1 f ⟩ , maybe some notation for singleton vector?
| open IsBasis hB | ||
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| private | ||
| BasisCat = MeetSemilatticeCategory (Basis→MeetSemilattice L L' hB) | ||
| DLCat = DistLatticeCategory L | ||
| BasisCat = ΣPropCat DLCat L' -- MeetSemilatticeCategory (Basis→MeetSemilattice L L' hB) |
| -- we get a pullback square in comm rings that then gives us the desired | ||
| -- square in R-algebras that we want to transport | ||
| theRingCospan = fgCospan R[1/ h ]AsCommRing (f /1) (g /1) | ||
| theRingPullback = fgPullback R[1/ h ]AsCommRing (f /1) (g /1) 1∈fgIdeal |
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One thing that we should also consider is splitting up the file Hopefully that would also speed up type-checking. What do you think @mortberg ? |
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This PR contains a proof that the structure presheaf defined on the basic opens of the Zariski lattice is indeed a sheaf.