[Merged by Bors] - feat(RingTheory/WittVector): ring of Witt vectors is p-adically complete#21295
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[Merged by Bors] - feat(RingTheory/WittVector): ring of Witt vectors is p-adically complete#21295
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PR summary baa25ed6ddImport changes for modified filesNo significant changes to the import graph Import changes for all files
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jcommelin
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…ete (#21295) In this PR, we show that if k is a perfect ring of char p, then the ring of Witt vectors is p-adically complete and p-torsion free.
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* factorial-dvd-int: (143 commits) Apply suggestions from code review feat(Factorial): k! divides the product of any k successive integers feat(CategoryTheory): creation of finite limits (#21320) chore: update Mathlib dependencies 2025-02-01 (#21328) chore(GroupTheory/SpecificGroups/Alternating.lean): follow last minute review of JX (#21314) feat: `‖x‖ₑ.toNNReal = ‖x‖₊` (#21306) chore: cleanup imports in Archive/IfNormalization (#21318) doc: fix several typos (#21315) feat(CategoryTheory): transfer being iso along an iso in the arrow category (#21310) chore: delete declarations deprecated between 2024-01 and 2024-07 (#21271) feat(Analysis/Normed/Module/Dual): polar in a normed space as a submodule (#20084) chore(Data/ZMod/Basic): split `ZMod.valMinAbs` off (#21308) feat(GroupTheory/Perm/Centralizer): study the centralizer of a permutation (#17522) feat(RingTheory/LocalRing): `IsLocalRing` for subrings (#21168) chore: update Mathlib dependencies 2025-02-01 (#21312) chore: update Mathlib dependencies 2025-01-31 (#21311) feat: generalize `mem_dite` to `Membership α β` (#21262) feat: Lemmas for some monomial orders (#16177) feat(CategoryTheory): the localized category is monoidal (#12728) feat: add function log⁺ (=positive part of the logarithm) and prove standard estimates (#21289) feat(RingTheory/WittVector): ring of Witt vectors is p-adically complete (#21295) feat(GroupTheory/GroupAction/Blocks): more on blocks (#21284) fix(FieldTheory/KrullTopology): make `krullTopology_discreteTopology_of_finiteDimensional` universe polymorphic (#21299) feat(RingTheory/Artinian): integral non-zero-divisors are units over artinian rings (#21199) refactor(Topology/Gluing): simplify definition of `TopCat.GlueData.Rel` (#20653) feat(RingTheory/PowerSeries): binomial series (#20192) chore(Mathlib/RingTheory/MvPolynomial): rename MonomiaOrder.lCoeff to MonomialOrder.leadingCoeff (#21290) chore (RingTheory/HahnSeries): fix names that use coeff (#21279) feat: let `notation3` distinguish `Prop` vs `Type _ ` vs `Sort _` (#21233) chore(MeasureTheory/Function/StronglyMeasurable): split Basic into Basic and AEStronglyMeasurable (#21273) feat(CategoryTheory): the monoidal category structure on a localization (#20951) feat(Analysis/Complex/Hadamard): generalize Hadamard's three lines theorem (#15009) feat(Order/CompleteBooleanAlgebra): Himp in terms of sSup (#20328) feat(ENNReal/Basic): add `ofNat_ne_top` and `top_ne_ofNat` (#14486) feat: Function.const as a PartialEquiv (#21137) chore(NonZeroDivisors): don't import rings (#20871) feat(Data/Set/Lattice): insert distributivity with iUnion/iInter (#21267) feat(GroupTheory/SpecificGroups/AlternatingGroup): subgroups of index 2 of Equiv.Perm (#21190) feat(GroupTheory/GroupAction/Transitive): basic results on transitive actions (#21285) perf(MeasureTheory/Function/LpSpace.lean): speed up (#21179) feat(Order): order isomorphisms from `Fin n` for small `n` (#21120) refactor(Topology/Group): turn morphisms in ProfiniteGrp into one field structures (#20740) feat: Sylow's first theorem for elementary `p`-groups (#21072) chore(Submonoid/Membership): don't import `MonoidWithZero` (#20748) refactor(Algebra/Algebra/Pi): cleanup and renaming (#21213) feat(GroupTheory/IndexNormal): subgroups of small index are normal (#21186) feat(Algebra/Group/Action): add definition of equidecomposition (#16936) feat(CategoryTheory/Subpresheaf): equalizer (#21096) feat: add lemmas about products of `Matrix.stdBasisMatrix` (#21204) chore: update Mathlib dependencies 2025-01-31 (#21282) ...
jt496
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…ete (#21295) In this PR, we show that if k is a perfect ring of char p, then the ring of Witt vectors is p-adically complete and p-torsion free.
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In this PR, we show that if k is a perfect ring of char p, then the ring of Witt vectors is p-adically complete and p-torsion free.