Motivic Landweber exactness.
Motivic symmetric spectra.
Motivic tubular neighborhoods.
Multiplicative maps from Hℤ to a ring spectrum R-a naive version
The paper is devoted to the study of the space of multiplicative maps from the Eilenberg-MacLane spectrum Hℤ to an arbitrary ring spectrum R. We try to generalize the approach of Schwede [Geom. Topol. 8 (2004)], where the case of a very special R was studied. In particular we propose a definition of a formal group law in any ring spectrum, which might be of independent interest.
Multiplicative operations in the Steenrod algebra for Brown–Peterson cohomology
A family of multiplicative operations in the BP Steenrod algebra is defined which is related to the total Steenrod power operation from the mod p Steenrod algebra. The main result of the paper links the BP versions of the total Steenrod power with the formal group approach to multiplicative BP operations by identifying the p-typical curves (power series) which correspond to these operations. Some relations are derived from this identification, and a short proof of the Hopf invariant one theorem...
Multiplicative properties of Atiyah duality.
On genera of polyhedra
We consider the stable homotopy category S of polyhedra (finite cell complexes). We say that two polyhedra X,Y are in the same genus and write X ∼ Y if X p ≅ Y p for all prime p, where X p denotes the image of Xin the localized category S p. We prove that it is equivalent to the stable isomorphism X∨B 0 ≅Y∨B 0, where B 0 is the wedge of all spheres S n such that π nS(X) is infinite. We also prove that a stable isomorphism X ∨ X ≅ Y ∨ X implies a stable isomorphism X ≅ Y.
On Neeman's well generated triangulated categories.
On real-oriented Johnson-Wilson cohomology.
On the Adams spectral sequence for -modules.
On the derivative of the stable homotopy of mapping spaces.
On the Detection of Some Elements in the Image of the Double Transfer Using K(2)-Theory.
On the homotopy inverse limits of transfer maps.
On the Iterated Complex Transfer.
On the plus construction for BGL Z [...] at the prime 2.
On the relationships between shape properties of subcompacta of and homotopy properties of their complements
Operations and co-operations in Morava -theory.
Periodic equivariant Real k-theories have rational Tate theory.
Phantom maps and purity in modular representation theory, I
Let k be a field and G a finite group. By analogy with the theory of phantom maps in topology, a map f : M → ℕ between kG-modules is said to be phantom if its restriction to every finitely generated submodule of M factors through a projective module. We investigate the relationships between the theory of phantom maps, the algebraic theory of purity, and Rickard's idempotent modules. In general, adding one to the pure global dimension of kG gives an upper bound for the number of phantoms we need...
Polynomial operations on stable cohomotopy.