A spectrum whose Zp cohomology is the algebra of reduced pth powers

Brown, Edgar H.; Peterson, Franklin P.

doi:10.1016/0040-9383(66)90015-2

Cited by 115 publications

(65 citation statements)

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“…Note that the analogue of the structure conjecture is true for ordinary topological BP (see Brown-Peterson [6]), and also in the Real case (see [12]). Note also that the structure conjecture would immediately imply Voevodsky's conjecture [26] on the existence of a spectral sequence from mod motivic cohomology to algebraic Morava K(n)-theory.…”

Section: Conjectures On M Glmentioning

confidence: 99%

Some Remarks on Real and Algebraic Cobordism

Hu¹,

Kříž²

2001

K-Theory

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Section: Conjectures On M Glmentioning

confidence: 99%

Some Remarks on Real and Algebraic Cobordism

Hu¹,

Kříž²

2001

K-Theory

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“…One can also define PLRQ's of M U [ 6 ] * giving rise to various versions of elliptic homology, but we refrain from giving details here. If we do not invert 6 then the relevant rings seem not to be LRQ's of M U * .…”

Section: Suppose Also That Pmentioning

confidence: 99%

Products on 𝑀𝑈-modules

Strickland

1999

Trans. Amer. Math. Soc.

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Abstract. Elmendorf, Kriz, Mandell and May have used their technology of modules over highly structured ring spectra to give new constructions of MUmodules such as BP , K(n) and so on, which makes it much easier to analyse product structures on these spectra. Unfortunately, their construction only works in its simplest form for modules over MU[ ] * that are concentrated in degrees divisible by 4; this guarantees that various obstruction groups are trivial. We extend these results to the cases where 2 = 0 or the homotopy groups are allowed to be nonzero in all even degrees; in this context the obstruction groups are nontrivial. We shall show that there are never any obstructions to associativity, and that the obstructions to commutativity are given by a certain power operation; this was inspired by parallel results of Mironov in Baas-Sullivan theory. We use formal group theory to derive various formulae for this power operation, and deduce a number of results about realising 2-local MU * -modules as MU-modules.

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“…In fact, one can show that α j l = 1 for all l, but it will be enough to know equation (6) for our purposes. It is well known that equation (5) holds for k = 0, see the original paper [3] or Theorem 4.1.12 in [6] for the mod p homology. Also, equation (6) is trivial in this case.…”

Section: Corollary There Are Canonical Isomorphisms Of a P -Modulesmentioning

confidence: 99%