Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 3rd 2017

    I finally created Hensel’s lemma, using the formulation in Bourbaki’s Commutative Algebra III.4.3. I also want to put in the formulation as alluded to in this M.SE answer to an old question of mine, which is more geometric.

    I also want to point out that at Henselian ring it might be worth expanding (and I can do this in a few weeks) to consider Henselian couples, where one no longer considers just the maximal ideal in a local ring, but any ideal contained in the radical. (This is a generalisation of the usual result in a different direction from Bourbaki’s, and no doubt one can form the pushout of these lemmas.) This point of view is very geometric.

    There is no doubt an interesting treatment using the internal language of an appropriate topos of this circle of ideas.

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 3rd 2017

    I also needed to create restricted formal power series, to describe one of the hypothesis of Bourbaki’s version of Hensel’s lemma.

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 3rd 2017

    I will actually type up the proof before too long. There are too many proofs on the internet of Hensel’s original lemma only.

    Ditto for Raynaud’s proof for characterisations of Henselian couples.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 11th 2017

    Added references at Hensel’s lemma.