├── .gitignore ├── .vscode └── settings.json ├── README.md ├── leanpkg.path ├── leanpkg.toml └── src ├── Kenny ├── gluing.lean ├── locally_ringed_space_on_opens.lean ├── projective_line.lean ├── sandbox.lean ├── sheaf_of_rings_on_opens.lean ├── sheaf_on_opens.lean ├── sites │ ├── basic.lean │ ├── lattice.lean │ ├── sheaf.lean │ └── type.lean └── subsheaf.lean ├── instances ├── affine_scheme.lean └── empty_scheme.lean ├── scheme.lean ├── sheaves ├── covering │ ├── covering.lean │ ├── covering_on_basis.lean │ └── covering_on_standard_basis.lean ├── locally_ringed_space.lean ├── presheaf.lean ├── presheaf_extension.lean ├── presheaf_maps.lean ├── presheaf_of_rings.lean ├── presheaf_of_rings_extension.lean ├── presheaf_of_rings_maps.lean ├── presheaf_of_rings_on_basis.lean ├── presheaf_on_basis.lean ├── sheaf.lean ├── sheaf_of_rings.lean ├── sheaf_of_rings_on_standard_basis.lean ├── sheaf_on_basis.lean ├── sheaf_on_standard_basis.lean ├── stalk.lean ├── stalk_of_rings.lean ├── stalk_of_rings_on_basis.lean ├── stalk_of_rings_on_standard_basis.lean └── stalk_on_basis.lean ├── spectrum_of_a_ring ├── induced_continuous_map.lean ├── induced_homeomorphism.lean ├── properties.lean ├── quasi_compact.lean ├── spec.lean ├── spec_locally_ringed_space.lean ├── standard_basis.lean ├── structure_presheaf.lean ├── structure_presheaf_localization.lean ├── structure_presheaf_res.lean ├── structure_presheaf_stalks.lean ├── structure_sheaf.lean ├── structure_sheaf_condition.lean ├── structure_sheaf_gluing.lean ├── structure_sheaf_locality.lean ├── strucutre_sheaf_stalks.lean └── zariski_topology.lean └── to_mathlib ├── finset_range.lean ├── ideals.lean ├── localization ├── local_rings.lean ├── localization_alt.lean ├── localization_ideal.lean ├── localization_of.lean ├── localization_of_iso.lean └── localization_tests │ ├── localisation_test_1.lean │ └── localisation_test_2.lean ├── opens.lean ├── ring_hom.lean └── topologcal_space.lean /.gitignore: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/.gitignore -------------------------------------------------------------------------------- /.vscode/settings.json: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/.vscode/settings.json -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/README.md -------------------------------------------------------------------------------- /leanpkg.path: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/leanpkg.path -------------------------------------------------------------------------------- /leanpkg.toml: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/leanpkg.toml -------------------------------------------------------------------------------- /src/Kenny/gluing.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/gluing.lean -------------------------------------------------------------------------------- /src/Kenny/locally_ringed_space_on_opens.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/locally_ringed_space_on_opens.lean -------------------------------------------------------------------------------- /src/Kenny/projective_line.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/projective_line.lean -------------------------------------------------------------------------------- /src/Kenny/sandbox.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/sandbox.lean -------------------------------------------------------------------------------- /src/Kenny/sheaf_of_rings_on_opens.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/sheaf_of_rings_on_opens.lean -------------------------------------------------------------------------------- /src/Kenny/sheaf_on_opens.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/sheaf_on_opens.lean -------------------------------------------------------------------------------- /src/Kenny/sites/basic.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/sites/basic.lean -------------------------------------------------------------------------------- /src/Kenny/sites/lattice.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/sites/lattice.lean -------------------------------------------------------------------------------- /src/Kenny/sites/sheaf.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/sites/sheaf.lean -------------------------------------------------------------------------------- /src/Kenny/sites/type.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/sites/type.lean -------------------------------------------------------------------------------- /src/Kenny/subsheaf.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/Kenny/subsheaf.lean -------------------------------------------------------------------------------- /src/instances/affine_scheme.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/instances/affine_scheme.lean -------------------------------------------------------------------------------- /src/instances/empty_scheme.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/instances/empty_scheme.lean -------------------------------------------------------------------------------- /src/scheme.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/scheme.lean -------------------------------------------------------------------------------- /src/sheaves/covering/covering.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/covering/covering.lean -------------------------------------------------------------------------------- /src/sheaves/covering/covering_on_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/covering/covering_on_basis.lean -------------------------------------------------------------------------------- /src/sheaves/covering/covering_on_standard_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/covering/covering_on_standard_basis.lean -------------------------------------------------------------------------------- /src/sheaves/locally_ringed_space.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/locally_ringed_space.lean -------------------------------------------------------------------------------- /src/sheaves/presheaf.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/presheaf.lean -------------------------------------------------------------------------------- /src/sheaves/presheaf_extension.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/presheaf_extension.lean -------------------------------------------------------------------------------- /src/sheaves/presheaf_maps.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/presheaf_maps.lean -------------------------------------------------------------------------------- /src/sheaves/presheaf_of_rings.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/presheaf_of_rings.lean -------------------------------------------------------------------------------- /src/sheaves/presheaf_of_rings_extension.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/presheaf_of_rings_extension.lean -------------------------------------------------------------------------------- /src/sheaves/presheaf_of_rings_maps.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/presheaf_of_rings_maps.lean -------------------------------------------------------------------------------- /src/sheaves/presheaf_of_rings_on_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/presheaf_of_rings_on_basis.lean -------------------------------------------------------------------------------- /src/sheaves/presheaf_on_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/presheaf_on_basis.lean -------------------------------------------------------------------------------- /src/sheaves/sheaf.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/sheaf.lean -------------------------------------------------------------------------------- /src/sheaves/sheaf_of_rings.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/sheaf_of_rings.lean -------------------------------------------------------------------------------- /src/sheaves/sheaf_of_rings_on_standard_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/sheaf_of_rings_on_standard_basis.lean -------------------------------------------------------------------------------- /src/sheaves/sheaf_on_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/sheaf_on_basis.lean -------------------------------------------------------------------------------- /src/sheaves/sheaf_on_standard_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/sheaf_on_standard_basis.lean -------------------------------------------------------------------------------- /src/sheaves/stalk.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/stalk.lean -------------------------------------------------------------------------------- /src/sheaves/stalk_of_rings.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/stalk_of_rings.lean -------------------------------------------------------------------------------- /src/sheaves/stalk_of_rings_on_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/stalk_of_rings_on_basis.lean -------------------------------------------------------------------------------- /src/sheaves/stalk_of_rings_on_standard_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/stalk_of_rings_on_standard_basis.lean -------------------------------------------------------------------------------- /src/sheaves/stalk_on_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/sheaves/stalk_on_basis.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/induced_continuous_map.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/induced_continuous_map.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/induced_homeomorphism.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/induced_homeomorphism.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/properties.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/properties.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/quasi_compact.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/quasi_compact.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/spec.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/spec.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/spec_locally_ringed_space.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/spec_locally_ringed_space.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/standard_basis.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/standard_basis.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/structure_presheaf.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/structure_presheaf.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/structure_presheaf_localization.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/structure_presheaf_localization.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/structure_presheaf_res.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/structure_presheaf_res.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/structure_presheaf_stalks.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/structure_presheaf_stalks.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/structure_sheaf.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/structure_sheaf.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/structure_sheaf_condition.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/structure_sheaf_condition.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/structure_sheaf_gluing.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/structure_sheaf_gluing.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/structure_sheaf_locality.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/structure_sheaf_locality.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/strucutre_sheaf_stalks.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/strucutre_sheaf_stalks.lean -------------------------------------------------------------------------------- /src/spectrum_of_a_ring/zariski_topology.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/spectrum_of_a_ring/zariski_topology.lean -------------------------------------------------------------------------------- /src/to_mathlib/finset_range.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/finset_range.lean -------------------------------------------------------------------------------- /src/to_mathlib/ideals.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/ideals.lean -------------------------------------------------------------------------------- /src/to_mathlib/localization/local_rings.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/localization/local_rings.lean -------------------------------------------------------------------------------- /src/to_mathlib/localization/localization_alt.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/localization/localization_alt.lean -------------------------------------------------------------------------------- /src/to_mathlib/localization/localization_ideal.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/localization/localization_ideal.lean -------------------------------------------------------------------------------- /src/to_mathlib/localization/localization_of.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/localization/localization_of.lean -------------------------------------------------------------------------------- /src/to_mathlib/localization/localization_of_iso.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/localization/localization_of_iso.lean -------------------------------------------------------------------------------- /src/to_mathlib/localization/localization_tests/localisation_test_1.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/localization/localization_tests/localisation_test_1.lean -------------------------------------------------------------------------------- /src/to_mathlib/localization/localization_tests/localisation_test_2.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/localization/localization_tests/localisation_test_2.lean -------------------------------------------------------------------------------- /src/to_mathlib/opens.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/opens.lean -------------------------------------------------------------------------------- /src/to_mathlib/ring_hom.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/ring_hom.lean -------------------------------------------------------------------------------- /src/to_mathlib/topologcal_space.lean: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ramonfmir/lean-scheme/HEAD/src/to_mathlib/topologcal_space.lean --------------------------------------------------------------------------------