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nLab > Latest Changes: lambda-ring

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  1.  
    • 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

  7. 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

1 to 7 of 7

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