chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
19,769 | lean_file_chunk | c283ed6087591a9dccd9d2f06169d601801d55b9e5e0cb2dd3c0cb87d89e6fd6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.Basic
public import Mathlib.RingTheory.RingHomProperties
/-!
# Constructors for properties of morphisms between ... |
7,684 | lean_file_chunk | e3ba5c23ba561e2f7ace49ab95d105f8a8ab362b18c5cab35a34c841ecd45c7b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.FiniteType
public import Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated
public import Mathlib.Algebr... |
4,764 | lean_file_chunk | c501434f0d3d897ffe0d554c6ea9252da49b2e64c90fe89a5edc47ccbbcdda51 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap
public import Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks
/-!
# Preimmersions of scheme... |
12,139 | lean_file_chunk | 8900fc319047d0de76223b80ce0b1a48bbed16697b1abdfa221b22d663046949 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.Proper
public import Mathlib.RingTheory.Ideal.IdempotentFG
public import Mathlib.RingTheory.RingHom.Unramified
pub... |
14,747 | lean_file_chunk | 1aa06835b49af44b80e937c0a6f021a6b2a71b1642ffcfa22b3db52f5d20e5e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.Affine
public import Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties
/-!
# Affine morphisms with ... |
21,007 | lean_file_chunk | ba6bd182045df6bbf1c957a865e03e70991c5aa0d22890282595754d8eb02aca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.Constructors
public import Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact
public import Mathlib.CategoryTheory.L... |
14,781 | lean_file_chunk | 0372227ca89c6c421a412a7afae22691241cb72994494cddd196abfccbcadbcb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated
public import Mathlib.AlgebraicGeometry.Morphisms.IsIso
public import Mathlib.AlgebraicGeometry.Pul... |
9,208 | lean_file_chunk | 9ccaa6e7d769af31bebe8c836bf8779229cd727f70de6cf9370a54119b8205fb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.Descent
public import Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed
public import Mathlib.Algebr... |
23,973 | lean_file_chunk | 7c8fd53082d2f0b4426926684ef52a82241e403b310fba702c54111cd301dcd4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
public import Mathlib.Algebra.CharP.Defs
/-!
# Some normal forms of elliptic curves
This file defines ... |
1,411 | lean_file_chunk | f7159ac6156915c43c35e26f2fc54bc2df6ee56deac404357e745e473fa66082 | lean_source_file | pkg_mathlib_source_file_chunks | theorem toCharTwoJNeZeroNF_spec (ha₁ : W.a₁ ≠ 0) :
(W.toCharTwoJNeZeroNF ha₁ • W).IsCharTwoJNeZeroNF := by
constructor
· simp [toCharTwoJNeZeroNF, ha₁, variableChange_a₁]
· simp [field, toCharTwoJNeZeroNF, variableChange_a₃, -mul_eq_zero]
linear_combination (W.a₃ * W.a₁ ^ 3 + W.a₁ ^ 2 * W.a₄ + W.a₃ ^ 2) *... |
17,204 | lean_file_chunk | eaa2e14c3d67965369c6469f173fc4f7a88f240236b02dcf77d056ee9ab76640 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, David Kurniadi Angdinata
-/
module
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Algebra.CubicDiscriminant
public import Mathlib.Tactic.FieldSimp
public... |
7,697 | lean_file_chunk | d408ff9b2f475daeca8846760475162bd9de5613acc0e0d3e2a91729691de5b5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, David Kurniadi Angdinata
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass
/-!
# Models of elliptic curves with prescribed j-invariant
This f... |
15,357 | lean_file_chunk | f561d5dcc684e611f6a35406c0c792a8392cf95335a85e22ab9ff566b218ab89 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms
public import Mathlib.FieldTheory.IsSepClosed
/-!
# Elliptic curves with same j-invariants are isomorphic
... |
11,857 | lean_file_chunk | 1ec991f188d1a71a795a2d3b897997d934ac6a246542f44499fbb695813b65f4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, David Kurniadi Angdinata, Jz Pan
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass
/-!
# Change of variables of Weierstrass curves
This file defines... |
14,730 | lean_file_chunk | 639bf92f95a41e8ccdb4c343bdf35f3d1d31befef19dee9ae59b7c2532f82d20 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bryan Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bryan Wang
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
public import Mathlib.RingTheory.DiscreteValuationRing.Basic
public import Mathlib.RingTheory.Loc... |
7,740 | lean_file_chunk | 4b0de4be4514a8b87b453ffe5b8c8636748e64b24d896c7c158ff54f228f372d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.AlgClosed.Basic
public import Mathlib.AlgebraicGeometry.Geometrically.Integral
public import Mathlib.Algeb... |
2,355 | lean_file_chunk | c838b2b4f1a33919e5ca81c3e86cb10aa62f6f99c3345983b33ea8c8832b1460 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.AlgClosed.Basic
public import Mathlib.AlgebraicGeometry.Morphisms.Smooth
public import Mathlib.CategoryTheory.Monoidal.Grp_
... |
4,803 | lean_file_chunk | ae7400d08b4e0296f3199f6eeada546a8793014eebdb5a4bcbd386f857a55d91 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.Finite
public import Mathlib.FieldTheory.IsAlgClosed.Basic
/-!
# Schemes over algebraically closed fields
We sho... |
23,995 | lean_file_chunk | 1978f5e37aac6b2f496f153edc092738dc1d215f87ad56470d85a2be1bef7cc2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.Preimmersion
public import Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated
public import Mathlib.AlgebraicGeome... |
12,847 | lean_file_chunk | 5b3fbecd9679cf7b0206477ed55ce7c71a0e639a20f3740163a6e2ff636665d9 | lean_source_file | pkg_mathlib_source_file_chunks | set_option backward.privateInPublic.warn false in
/-- The subscheme associated to an ideal sheaf `I` is covered by `Spec(Γ(X, U)/I(U))`. -/
noncomputable
def subschemeCover : I.subscheme.AffineOpenCover where
I₀ := X.affineOpens
X U := .of <| Γ(X, U) ⧸ I.ideal U
f U := I.glueData.ι U ≫ I.subschemeIso.inv
idx x ... |
23,994 | lean_file_chunk | 2f2b4834354ca8be6c5098ec8576903fe9ffefb1cfb83c4867cba05bda0bc3c9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact
public import Mathlib.AlgebraicGeometry.Properties
public import Mathlib.Tactic.DepRewrite
/-!
# Ide... |
15,302 | lean_file_chunk | 4ac9b84e050b2105f8f91309daba4461ef754226bab9826425fea41e0ef908f1 | lean_source_file | pkg_mathlib_source_file_chunks | · letI : Algebra Γ(X, U) Γ(X, X.affineBasicOpen f) := F.hom.toAlgebra
have : IsLocalization.Away f Γ(X, X.basicOpen f) :=
U.2.isLocalization_of_eq_basicOpen _ _ rfl
intro x hx
dsimp only at hx ⊢
have : Topology.IsOpenEmbedding (Spec.map F) :=
localization_away_isOpenE... |
3,971 | lean_file_chunk | bf9b545d76b666a592713ac64d326550179d81839c67c6c0439f2d6f6148b341 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Thomas Browning, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion
public import Mathlib.AlgebraicGeometry.Noetherian
/-!
# Subsch... |
9,302 | lean_file_chunk | 093442889005288c9acc124eb8bb1fed7edd42a6ecb4c81822a3cfffa66f7c11 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion
public import Mathlib.AlgebraicGeometry.PullbackCarrier
/-!
# Functorial constructions of ideal s... |
8,055 | lean_file_chunk | eb78e6d869fbe5f6fc44de1f6ac5b9513831090356c2c1380c0aec3293b4b236 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Joël Riou, Ravi Vakil
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Representable
public import Mathlib.AlgebraicGeometry.Sites.BigZariski
public import Ma... |
5,407 | lean_file_chunk | edc38237bc765b4ae19bb9ff0e14299d05138ec8383f257704ea8b219be2ba49 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.EffectiveEpi
public import Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen
public import Mathlib.AlgebraicGeom... |
5,462 | lean_file_chunk | 7af0e3d9d66af506e4d63b1c20d7b71c644aaa59ba55220b6ad9e0b07b1a6c97 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Sites.MorphismProperty
public import Mathlib.AlgebraicGeometry.PullbackCarrier
/-!
# Grothendieck topology define... |
9,289 | lean_file_chunk | 7dc362debf78ec6270141827bfffdc039f566015d0380cdaa20290f6244e6cb0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily
public import Mathlib.AlgebraicGeometry.Sites.BigZariski
public import Mathlib.AlgebraicG... |
7,051 | lean_file_chunk | 968a1c9f920a03b1e3ae19bb3f6a9f69a135f4ea90b02cba22af1d6c4b2528de | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Adam Topaz
-/
module
public import Mathlib.AlgebraicGeometry.Cover.Sigma
public import Mathlib.AlgebraicGeometry.Sites.Pretopology
public import Mathlib.CategoryTheory.Sites.Cop... |
5,233 | lean_file_chunk | ed8929f4d60391f37e7d376ef51e8d042aa741378273dfbdd301d69d14ec0ec9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Sites.QuasiCompact
/-!
# Sheaves for the quasi-compact topology
In this file we show that a presheaf is a sheaf ... |
3,023 | lean_file_chunk | ab2443c0d435f3745dd45c999136267faffddda94420a8ab6feb5984b8b9506e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.Etale
public import Mathlib.AlgebraicGeometry.Sites.BigZariski
public import Mathlib.AlgebraicGeometry.S... |
6,985 | lean_file_chunk | 0dc6c2e6a688a89bea416ef6e8ea5fda4278fdd29eac41b5804440745c0e211e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jiedong Jiang, Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang, Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen
public import Mathlib.AlgebraicGeometry.Morphisms.WeaklyEt... |
5,145 | lean_file_chunk | d6663fb0b36fd48ba8e05347df760f8f4a1989d026133739538ab00e832ef673 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Sites.Fpqc
public import Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Terminal
/-!
# Sheaf of continuous ... |
3,427 | lean_file_chunk | 2b57d69731ac6973464c61dbf9f2a22669e7839216e2365b66b309c14023d449 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang, Christian Merten
-/
module
public import Mathlib.Algebra.Category.Grp.AB
public import Mathlib.Algebra.Category.Grp.Ulift
public import Mathlib.AlgebraicGeometry.Site... |
11,815 | lean_file_chunk | 7bf4703a8af763e3306111aa15db0d6f5e464017b28dc2eaf4792aeaeff66fcf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Cover.Over
public import Mathlib.AlgebraicGeometry.Sites.Pretopology
public import Mathlib.CategoryTheory.Sites.De... |
5,320 | lean_file_chunk | 4cd3c8cf8c392b8f4404558a00cf3d1b04d5af0700763b0370e78c7648e3f2d3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten, Joël Riou, Adam Topaz
-/
module
public import Mathlib.AlgebraicGeometry.OpenImmersion
public import Mathlib.CategoryTheory.MorphismProperty.Limits
public import Ma... |
16,829 | lean_file_chunk | 97d4b2d6cc88064d9f56ab16aaf2d40b3771f4c4a08a0ef2a9ae7d54d82eb7b9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.AffineScheme
public import Mathlib.AlgebraicGeometry.RelativeGluing
public import Mathlib.CategoryTheory.Sites.DenseSubsite.... |
17,778 | lean_file_chunk | 05ec1dcdfb3209d4d2830278866d53327a23f7eff6d926a99641a5e143720f3f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Johan Commelin
-/
module
public import Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal
public import Mathlib.Topology.Category.TopCat.Basic
public import Mathlib.Topolo... |
23,922 | lean_file_chunk | 455366778d560abee46fbc5f7195f0ffe925c7e12077265afeaacebdb18420c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme
public import Mathlib.AlgebraicGeometry.AffineScheme
public import Mathlib.AlgebraicGeometry.Gluin... |
304 | lean_file_chunk | 2c7f2517cdba0fc27fac5a4528cda9652c29ca8be1d6385dfac10cd323a3f0cb | lean_source_file | pkg_mathlib_source_file_chunks | IsOpenImmersion.isoOfRangeEq_inv_fac_assoc, ← HomogeneousLocalization.algebraMap_eq]
congr 2
rw [RingHom.comp_assoc, ← IsScalarTower.algebraMap_eq, IsScalarTower.algebraMap_eq _ A,
← RingHom.comp_assoc, IsLocalization.map_comp, RingHom.comp_assoc]
end ofGlobalSection
end AlgebraicGeometry.Proj |
16,516 | lean_file_chunk | 45d6a549f6d62b499ac123002ca77eb6f44f2feb07c937a88f2811235d20c418 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology
public import Mathlib.Topology.Sheaves.LocalPredicate
public import Mathlib.RingTheory.GradedA... |
17,208 | lean_file_chunk | 96b926b5ef2b6afa2cf83872d30463df8046499b007e98a473f6c323fe058519 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patience Ablett, Kevin Buzzard, Harald Carlens, Wayne Ng Kwing King, Michael Schlößer,
Justus Springer, Andrew Yang, Jujian Zhang
-/
module
public import Mathlib.Algebra.Order.BigOpera... |
23,985 | lean_file_chunk | 7a15bb720dd4772212026275e381f267670110fe866c1ef35e52caead83d4ced | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf
public import Mathlib.AlgebraicGeometry.GammaSpecAdjunction
public import M... |
15,838 | lean_file_chunk | f7dc4eb28c7d2abb09543f96ecd2d9a07d79eca20bcecb89aa8477f0fdedb51b | lean_source_file | pkg_mathlib_source_file_chunks | rw [Opens.carrier_eq_coe, toSpec_preimage_basicOpen, ProjectiveSpectrum.basicOpen_pow 𝒜 _ m hm]
end toSpec
set_option backward.isDefEq.respectTransparency false in
variable {𝒜} in
/-- The continuous function `Spec A⁰_f → Proj|D(f)` sending `q` to `{a | aᵢᵐ/fⁱ ∈ q}` where
`m` is the degree of `f` -/
def fromSpec {f ... |
9,065 | lean_file_chunk | 8636bfddcb5c30393a21762589fb61aa4fc847b668291d043fb0b13009d17e87 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic
public import Mathlib.RingTheory.GradedAlgebra.Homogeneous.Maps
/-! # Functoriality of Proj -/
@[exp... |
5,400 | lean_file_chunk | 23aff7bc8a5ef0726585ebd26dffebf2270d9d36c64d0db161e39364adc2ae0b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Geometrically.Reduced
public import Mathlib.AlgebraicGeometry.Geometrically.Irreducible
/-!
# Geometrically Integral Scheme... |
6,298 | lean_file_chunk | e9e569f3f7167cc9eaf7846fb4a2fa670651910eb546c59995f364af46c52e9b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Timo Kraenzle, Judith Ludwig, Bryan Wang, Christian Merten,
Yannis Monbru, Alireza Shavali, Chenyi Yang
-/
module
public import Mathlib.AlgebraicGeometry.Properties
public import ... |
5,367 | lean_file_chunk | 86e7edbb4b8f0104e5b1080e3ea558a5e2ba4e220c7780a7b6f931fca42edd6f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Timo Kraenzle, Judith Ludwig, Bryan Wang, Christian Merten,
Yannis Monbru, Alireza Shavali, Chenyi Yang
-/
module
public import Mathlib.AlgebraicGeometry.Geometrically.Basic
publi... |
6,902 | lean_file_chunk | 09bf7082dd747b49ad20e3ad087db09ceb4eff836f993bc0b21cd17252e38161 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Geometrically.Basic
public import Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen
/-!
# Geometrically Irreducible Schem... |
5,990 | lean_file_chunk | c3d48ffd5f8a61ed7cb1e1babc17597d25ff206dfc05f61c3d687577eb07bed9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Artinian
public import Mathlib.AlgebraicGeometry.Geometrically.Basic
public import Mathlib.AlgebraicGeometry.Morphisms.Schem... |
1,431 | lean_file_chunk | 9cdbbecbd746db6224172f35a416c6624ab45801daa1ba33f46caa8b3e00c12a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Presheaf
public import Mathlib.AlgebraicGeometry.Scheme
public import Mathlib.CategoryTheory.Sites.Whiskering
/-!
# Th... |
20,086 | lean_file_chunk | ccca6736f7d1e1b5978f45b801ee039d5d978f8c8746a8d5be2afd59fcc6212d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Andrew Yang
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian
public import Mathlib.Algebra.Category.ModuleCat.Sheaf.Colimits
public import Mathlib.Algebr... |
19,427 | lean_file_chunk | 40636e35ccbb170fe3852287e8a857a355be5c51d5a254968bf3a6a3d47e2ca6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Weihong Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Johan Commelin, Amelia Livingston, Sophie Morel, Jujian Zhang, Weihong Xu,
Andrew Yang
-/
module
public import Mathlib.Algebra.Module.LocalizedModule.Basic
public import ... |
10,989 | lean_file_chunk | ed74bb1794539754e6cd165825200ab048e4e5b9b9c175b9083bc24d17d6fde1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.Affine
public import Mathlib.AlgebraicGeometry.Properties
public import Mathlib.AlgebraicGeometry.Pullba... |
2,755 | lean_file_chunk | a5380a74847c9090f5d42e501459d19caec5456219e006518be70cb3c213830a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.Basic
/-!
# Collapsing covers
We define the endofunctor on `Scheme.Cover P` that collapses a cover to ... |
8,930 | lean_file_chunk | 3e3f3d2ca5741bd1704611f907c1aa4eac23b0f5870659200d213ff5804e47be | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap
public import Mathlib.CategoryTheory.Limits.MorphismProperty
/-!
# Covers of schemes ove... |
13,539 | lean_file_chunk | 2460473279a37d7379dd89337f5dfc093acb5f7d958dd43218369a8cdbce073c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Cover.MorphismProperty
/-!
# Open covers of schemes
This file provides the basic API for open covers of schemes.
## Main ... |
9,866 | lean_file_chunk | 878683c0e5a6868039705f6680b564249dcc05d4b79e96246e64c23c4712b2bb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten, Andrew Yang
-/
module
public import Mathlib.AlgebraicGeometry.Sites.MorphismProperty
public import Mathlib.CategoryTheory.MorphismProperty.Limits
/-!... |
14,164 | lean_file_chunk | 59b2c408cbf727b1f10761d8a76df9fe98700633b4b0810f795c4365ed7614c4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.LocallyDirected
public import Mathlib.AlgebraicGeometry.PullbackCarrier
public import Mathlib.AlgebraicGeometry.Gluin... |
23,956 | lean_file_chunk | 0c32c9f3bb7e89088a4e0f5d4397472355d42bef310a90d41415eada46a36b13 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
public import Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula
... |
6,207 | lean_file_chunk | cda501950e127e1ca00ad7c937f7cc8958bd964e11f768cce79d0964d430c1c5 | lean_source_file | pkg_mathlib_source_file_chunks | · rw [add_of_Z_eq_zero_left hP.left hPz hQz,
toAffine_smul _ <| (isUnit_X_of_Z_eq_zero hP hPz).mul <| Ne.isUnit hQz]
· by_cases hQz : Q z = 0
· rw [add_of_Z_eq_zero_right hQ.left hPz hQz,
toAffine_smul _ ((isUnit_X_of_Z_eq_zero hQ hQz).mul <| Ne.isUnit hPz).neg,
toAffine_of_Z_eq_zero hQz, ... |
23,963 | lean_file_chunk | 6165f769d198152758ea656acad202b3893dedbdcb1dbd7e3bf978172000fb77 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.Algebra.MvPolynomial.PDeriv
public import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic
public import Mathlib... |
2,688 | lean_file_chunk | 3901da3ad1665ff8545a198a1642180bc36b0ffbfd2685231eff9a1c02579d1a | lean_source_file | pkg_mathlib_source_file_chunks | lemma map_equation (hf : Function.Injective f) :
(W'.map f).toJacobian.Equation (f ∘ P) ↔ W'.Equation P := by
simp only [Equation, map_polynomial, eval_map, ← eval₂_comp, map_eq_zero_iff f hf]
@[simp]
lemma map_polynomialX : (W'.map f).toJacobian.polynomialX = MvPolynomial.map f W'.polynomialX := by
simp only ... |
23,952 | lean_file_chunk | f9fdb96aa4f78ff59f942fd73a55f4dcc135cec75d7e41dde051240fec67c014 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula
public import Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Basic
... |
15,023 | lean_file_chunk | f9d8744e6f965249409df9e271dd252f988584de94aa7bab21440108c51eb72c | lean_source_file | pkg_mathlib_source_file_chunks | - Q x * P z ^ 2 * addZ P Q ^ 2) / (P z * Q z) ^ 2 := by
rw [← addX_eq' hP hQ, mul_div_cancel_right₀ _ <| pow_ne_zero 2 <| mul_ne_zero hPz hQz]
lemma addX_smul (P Q : Fin 3 → R) (u v : R) :
W'.addX (u • P) (v • Q) = ((u * v) ^ 2) ^ 2 * W'.addX P Q := by
simp only [addX, smul_fin3_ext]
ring1
lemma addX_self {... |
18,236 | lean_file_chunk | 54a62ad62ff290d6907a2459f441adb474ba468f135b638776efc1230ee4a879 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
public import Mathlib.NumberTheory.EllipticDivisibilitySequence
/-!
# ... |
19,142 | lean_file_chunk | 6e491b5008a1aa2106f1da27630db39df19e0c9214f2ee1ad814df14007a5aa2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic
public import Mathlib.Tactic.ComputeDegree
/-!
# Division ... |
23,979 | lean_file_chunk | 76913368f3b07e5f0d4671c85dac176d6d94efdd67350b22ffc056e8c0f2bf3c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula
public import Mathlib.LinearAlgebra.FreeModule.Norm
public import Mat... |
14,902 | lean_file_chunk | 0465082c7147fdd9cd8b4bb4848148aa7195e622288229632a3383c3e3aa4ab3 | lean_source_file | pkg_mathlib_source_file_chunks | left_inv := by rintro (_ | _) <;> rfl
right_inv := by rintro (_ | _) <;> rfl
@[simp]
lemma nonsingularPointEquivSubtype_zero {p : W'.Point → Prop} (p0 : p .zero) :
nonsingularPointEquivSubtype p0 ⟨.zero, p0⟩ = none :=
rfl
@[simp]
lemma nonsingularPointEquivSubtype_some {x y : R} {h : W'.Nonsingular x y} {p : ... |
12,792 | lean_file_chunk | ebbfc8e9cce7599ffb8700ff4b174a641a92c8e9a7a30fad0ad6a7c066401191 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.Algebra.Polynomial.Bivariate
public import Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
/-!
# Weierstrass... |
20,230 | lean_file_chunk | 135d6e7508915b5aa89e35ee2eb9853f52bd331b5bfa480cd822e96e6e4c3209 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic
/-!
# Negation and addition formulae for nonsingular points in affine ... |
23,935 | lean_file_chunk | 902399f071920322d56b4494656b53a2bd1253cbfbe1ef01789ebda387d40b4e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
public import Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formul... |
5,391 | lean_file_chunk | 3324cc59e7a84a162f0294981f6d1a73bf5d28911b04f9c0377d52021f634fd0 | lean_source_file | pkg_mathlib_source_file_chunks | toAffine_smul _ <| isUnit_addU_of_Y_ne hPz hQz hy, toAffine_zero]
· have := toAffine_add_of_Z_ne_zero hP hQ hPz hQz hxy
by_cases hx : P x * Q z = Q x * P z
· rwa [add_of_Y_ne' hP.left hQ.left hPz hQz hx <| not_and.mp hxy hx,
toAffine_smul _ <| isUnit_dblZ_of_Y_ne' hP.left hQ.left hPz h... |
23,992 | lean_file_chunk | d6570a96f47e21948af9523f443dcc0a714d5d87c861c0436fed8a82bde2a53d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.Algebra.MvPolynomial.PDeriv
public import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic
public import Mathlib... |
1,078 | lean_file_chunk | 2bfaad4b0d51947b0e2e2d1e050add750e0cfdc25cdc040dfbb56267ef3be9ff | lean_source_file | pkg_mathlib_source_file_chunks | (W'.baseChange B).toProjective.Equation (f ∘ P) ↔
(W'.baseChange A).toProjective.Equation P := by
rw [← RingHom.coe_coe, ← map_equation P hf, AlgHom.toRingHom_eq_coe, map_baseChange]
lemma baseChange_polynomialX : (W'.baseChange B).toProjective.polynomialX =
MvPolynomial.map f (W'.baseChange A).toProjectiv... |
23,968 | lean_file_chunk | 19d9fe3712b9b5c4deb017cb872cc14cc6e8d65e3e36fe72e69982232d2ee715 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
module
public import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula
public import Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basi... |
23,161 | lean_file_chunk | 58cc97559259df0afdd0c34962795f08b0e210612cc6f45b1815d2d2b138976f | lean_source_file | pkg_mathlib_source_file_chunks | lemma dblXYZ_Y (P : Fin 3 → R) : W'.dblXYZ P y = W'.dblY P :=
rfl
lemma dblXYZ_Z (P : Fin 3 → R) : W'.dblXYZ P z = W'.dblZ P :=
rfl
lemma dblXYZ_smul (P : Fin 3 → R) (u : R) : W'.dblXYZ (u • P) = u ^ 4 • W'.dblXYZ P := by
rw [dblXYZ, dblX_smul, dblY_smul, dblZ_smul, smul_fin3, dblXYZ_X, dblXYZ_Y, dblXYZ_Z]
lem... |
2,190 | lean_file_chunk | ca3665408c3bd38b5ccfce6429a571cb5457c7515b8e877e1f1e6c1045fb052e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Stepan Nesterov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stepan Nesterov
-/
module
public import Mathlib.Algebra.Lie.OfAssociative
public import Mathlib.FieldTheory.IsAlgClosed.Basic
/-!
# Basic facts about algebra representations
This f... |
11,789 | lean_file_chunk | a45996dd12fbae746700208740e49325eb25ba72651c865906369f5db2f6016f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Homology.AlternatingConst
public import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
public import Mathlib.CategoryTheo... |
21,245 | lean_file_chunk | 569b3a045ae8dfe1ed51c28d5080836d6259ba0d394c7bfc02e042b67678e6ad | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Adjunctions
public import Mathlib.AlgebraicTopology.ExtraDegeneracy
public import Mathlib.CategoryTheor... |
3,452 | lean_file_chunk | 96701dbb208928aa0cbab8987b8cea6f3c45ab53c082e46859b29ad71ceb2607 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yunzhou Xie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Edison Xie
-/
module
public import Mathlib.RepresentationTheory.Rep.Basic
/-!
# Restriction of representations
Given a group homomorphism `f : H →* G`, we have the restriction functor
`... |
23,966 | lean_file_chunk | dde9591341df0d5c1cc69e1f515a5309da0fd1b32035f22d1204b86d5dbc4629 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yunzhou Xie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Edison Xie, Kim Morrison
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Abelian
public import Mathlib.Algebra.Category.ModuleCat.Colimits
public import Mathlib.Representation... |
13,347 | lean_file_chunk | da48a75c6fc566bbe7e3dc5b65b3c8b39da26d99a3655509ade5d623b0462d81 | lean_source_file | pkg_mathlib_source_file_chunks | (Representation.TensorProduct.lid k X.ρ).toIntertwiningMap :=
rfl
@[simp]
lemma hom_inv_leftUnitor {X : Rep k G} : (λ_ X).inv.hom =
(Representation.TensorProduct.lid k X.ρ).symm.toIntertwiningMap := rfl
@[simp]
lemma hom_hom_rightUnitor {X : Rep k G} : (ρ_ X).hom.hom =
(Representation.TensorProduct.rid k X.... |
9,314 | lean_file_chunk | 32b741c8e4f4478b3d388ac8137bd7143606a25bcc8fe1d41629ec65c1452414 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yunzhou Xie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Edison Xie
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Projective
public import Mathlib.RepresentationTheory.Rep.Basic
/-!
# Equivalence between `Rep k G` and `ModuleCat ... |
8,020 | lean_file_chunk | c2e87221662bcc8e2ad7e579fad4f1a071c9f29a6ce66ddd9c4e1678e384dde3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Homology.ConcreteCategory
public import Mathlib.Algebra.Homology.HomologicalComplexAbelian
public import Mathlib.Represent... |
23,963 | lean_file_chunk | ee7b2ba61ef03ac822c50ee8d647a69346b18b05df885e6b02126c5969b13435 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree
/-!
# Functoriality of group homology
Given a commutative ring `k`, a g... |
15,771 | lean_file_chunk | 4640e1b60269df27ecc5fb88cc7cfd5274f66b1c29e1501497dceddc5a3114ce | lean_source_file | pkg_mathlib_source_file_chunks | of `A` spanned by elements of the form `ρ(s)(a) - a` for `s : S, a : A`. Then the image of
`C₁(G, I(S)A)` in `C₁(G, A)⧸B₁(G, A)` is contained in the image of `C₁(S, A)`. -/
theorem comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top :
Submodule.comap ((mapShortComplexH1 (MonoidHom.id G) (coinvariantsShor... |
8,247 | lean_file_chunk | 6f1febc1c51cdbffb06e16b49a94cae6381a965fbec8b9ce30607a7a97ec169f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.RepresentationTheory.Homological.FiniteCyclic
public import Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree
/-!
... |
11,612 | lean_file_chunk | 6c9515f6bdeb9dba40533d555917748f28b5bf941405090b59c62ad4fded97fc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Homology.ConcreteCategory
public import Mathlib.RepresentationTheory.Coinvariants
public import Mathlib.RepresentationTheo... |
3,370 | lean_file_chunk | f5243cd3191320419475ea9c3a4168ada5abd98e7d249d6c038fb59d61a6097c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.CategoryTheory.Preadditive.Projective.Resolution
public import Mathlib.RepresentationTheory.Homological.GroupHomology.Basic
public... |
23,965 | lean_file_chunk | 88ab299835c01d658fdbadd2518b0eed39c7d5f0808fb378d9135d7010531c7f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
public import Mathlib.GroupTheory.Abelianization.Defs
public import Mathlib.Representation... |
20,149 | lean_file_chunk | 40bab7816a3661d67d3e2d7381f80e2245c96ad4afd9fc683e0a0569626b8a7b | lean_source_file | pkg_mathlib_source_file_chunks | simpa using (mem_cycles₁_iff (A := Rep.ofDistribMulAction k G A) x).1 hx
/-- Given a `k`-module `A` with a compatible `DistribMulAction` of `G`, and a finsupp
`x : G →₀ A` satisfying the 1-boundary condition, produces a 1-boundary for the representation
on `A` induced by the `DistribMulAction`. -/
@[simps]
def boundar... |
8,232 | lean_file_chunk | 924759f2165dfc74e3c8bc0445a5a80180d0f69146eb988112a295192ad38835 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Homology.ConcreteCategory
public import Mathlib.Algebra.Homology.HomologicalComplexAbelian
public import Mathlib.Represent... |
22,187 | lean_file_chunk | 995100dce0641e6f42dca1efc1dda84be50a87f564b3cf21f31720f4a35f176d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic
public import Mathlib.RepresentationTheory.Homological.GroupCohomology.LowD... |
7,431 | lean_file_chunk | 15364be8681ebbac197a93f1460eb78791a3dbca38ac242d90d1f61a4ec88ad9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.RepresentationTheory.Homological.FiniteCyclic
public import Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree
/-... |
9,560 | lean_file_chunk | 12af724ca6a6af8f2b34a980f22bf4259bbf743a94fbc8affff8ff30f9c58d7d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Homology.Opposite
public import Mathlib.Algebra.Homology.ConcreteCategory
public import Mathlib.RepresentationTheory.Homol... |
9,939 | lean_file_chunk | 0856b4d4048265fb28f92f834c16a0ec68bf3fe53d65af4a1d719f64734fc713 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Amelia Livingston
-/
module
public import Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic
public import Mathlib.RingTheory.IntegralClosure.In... |
2,983 | lean_file_chunk | 24be51ca93cd5ae9a40be3bae3b2f6f8593f8da415a40c1828e837fdf07434fe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.CategoryTheory.Preadditive.Projective.Resolution
public import Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic
publ... |
23,984 | lean_file_chunk | ec3e5dc9351a43c3a051429f867eecaa196bcc5b7eb4415110bf62d7a434f098 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Joël Riou
-/
module
public import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
public import Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic
pu... |
17,964 | lean_file_chunk | 7fadc3ee8fe35819141951a8e0f82b005aec6439d64a7248a49c183db09f51ab | lean_source_file | pkg_mathlib_source_file_chunks | g • f g⁻¹ = (f g)⁻¹ := by
rw [← mul_eq_one_iff_eq_inv, ← map_one_of_isMulCocycle₁ hf, ← mul_inv_cancel g, hf g g⁻¹]
theorem smul_map_inv_div_map_inv_of_isMulCocycle₂
{f : G × G → M} (hf : IsMulCocycle₂ f) (g : G) :
g • f (g⁻¹, g) / f (g, g⁻¹) = f (1, 1) / f (g, 1) := by
have := hf g g⁻¹ g
simp only [mul_... |
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