Twisting lemma for $\lambda$-adic modules

Fitting’s Lemma for Z/2-graded Modules

Let φ : Rm → Rd be a map of free modules over a commutative ring R. Fitting’s Lemma shows that the “Fitting ideal,” the ideal of d × d minors of φ, annihilates the cokernel of φ and is a good approximation to the whole annihilator in a certain sense. In characteristic 0 we define a Fitting ideal in the more general case of a map of graded free modules over a Z/2graded skew-commutative algebra a...

Hensel’s lemma, valuations, and p-adic numbers

A VAN DER CORPUT LEMMA FOR THE p-ADIC NUMBERS

We prove a version of van der Corput's Lemma for polynomials over the p-adic numbers.

On Adic Genus and Lambda-rings

Sufficient conditions on a space are given which guarantee that the K-theory ring is an invariant of the adic genus. An immediate consequence of this result about adic genus is that for any positive integer n, the power series ring Z[[x1, . . . , xn]] admits uncountably many pairwise non-isomorphic λ-ring structures.

Adic Genus , Postnikov Conjugates , and Lambda - Rings

Sufficient conditions on a space are given which guarantee that the K-theory ring and the ordinary cohomology ring with coefficients over a principal ideal domain are invariants of, respectively, the adic genus and the SNT set. An independent proof of Notbohm’s theorem on the classification of the adic genus ofBS by KO-theory λ-rings is given. An immediate consequence of these results about adi...