Not signed in (Sign In)

Start a new discussion

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 beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics planar 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 string string-theory subobject 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.
    • CommentAuthorStephan A Spahn
    • CommentTimeMay 29th 2012
    • (edited May 29th 2012)

    I edited lambda-ring, added a definition from the thesis of John R. Hopkins. Later on I will add the definitions of Hazewinkel, too. This entry has a long (and very instructive) idea-section. Maybe I find time to fill in some more details to these ideas.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeMay 29th 2012

    Thank you, this is very important topic we should have more in nnLab. John Baez was at some time interested, I think some of his ideas deserve more thought, and of course, now it is very actual with the developments in absolute algebraic geometry.

    • CommentRowNumber3.
    • CommentAuthorStephan A Spahn
    • CommentTimeMay 31st 2012
    • (edited May 31st 2012)

    Maybe I find time to fill in some more details to these ideas.

    I have done this now: lambda-ring. What was explained in prose I wrote in a more formal (looking) way. I also split the section containing the reading guide to Hazewinkel’s article from the main article. What is still on the to-do list is to merge lambda ring and special lambda-ring.

    • CommentRowNumber4.
    • CommentAuthorAndrew Stacey
    • CommentTimeJun 1st 2012

    Couple of queries on this page. First, a minor one: I found a thesis due to a John Hopkinson, not John Hopkins. Do I have the right person (perhaps adding to the confusion is that the supervisor was Mike Hopkins)?1

    More importantly, Wilkerson’s theorem is stated as:

    Let AA be an additively torsion-free commutative ring. Let {ψ p}\{\psi_p\} be a commuting family of Frobenius lifts.

    Then there is a unique λ\lambda-ring structure on AA whose Adams operations are the given Frobenius lifts {ψ p}\{\psi_p\}.

    This is certainly true rationally, but I’m not sure that it is true integrally. The relationship between the Adams’ operations and the lambda operations is that the nnth lambda operation is determined by the Adams’ operations (and lower lambda operations) upto a multiplier of n!n!. The correct statement (I believe) is that the Adams operations determine the lambda operations in the torsion-free setting, so long as they are already there. Hopkinson’s thesis states it this way, I’m unable to get a (free, electronic) copy of Wilkerson’s original paper to see what this contained.

    1. Evidence for this is supplied by the fact that the link to the PDF on the page lambda ring has changed to its “visited” form after I downloaded John Hopkinson’s thesis via another route. 

    • CommentRowNumber5.
    • CommentAuthorAndrew Stacey
    • CommentTimeJun 1st 2012

    Hmm, maybe there’s something about the ψ p\psi_p being Frobenius lifts that makes all the difference. Haven’t yet tracked down a detailed proof, though.

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeSep 13th 2018

    Fixed an internal link.

    diff, v39, current

  1. The collection of power series with constant coefficient 1 should be written as 1+tRt and not 1+Rt as it is was originally written.

    Kapil Paranjape

    diff, v41, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)