For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel cohomology Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and duality, are shown to lift to the category of modules over the associated Steenrod algebra. The dependence on the dimension functions of the representations i...

We show that the category of rational G-spectra for a torus G is Quillen equivalent to an explicit small and practical algebraic model, thereby providing a universal de Rham model for rational G-equivariant cohomology theories. The result builds on the Adams spectral sequence of [12], the enriched Morita equivalences of [23], and the functors of [27] making rational spectra algebraic.

This paper proves the existence of a new nontrivial family of filtration three in the stable homotopy group of spheres p2ð p nþpÞð p 1Þ 3S which is of order p and is represented by (b0hn þ h1bn 1Þ in the E 3; 2ð p þpÞð p 1Þ 2 -term of the Adams spectral sequence, where pb 5 is a prime and nb 3.

We use homological ideals in triangulated categories to get a sufficient criterion for a pair of subcategories in a triangulated category to be complementary. We apply this criterion to construct the Baum–Connes assembly map for locally compact groups and torsion-free discrete quantum groups. Our methods are related to the abstract version of the Adams spectral sequence by Brinkmann and Christe...

This paper constructs a new family in the stable homotopy of spheres πt−6S represented by hng0γ3 ∈ E 2 in the Adams spectral sequence which revisits the bn−1g0γ3-elements ∈ πt−7S constructed in [3], where t = 2pn(p− 1) + 6(p + p + 1)(p− 1) and p ≥ 7 is a prime, n ≥ 4.

This paper presents some speculations about alternatives to the recently disproved telescope conjecture in stable homotopy theory. It includes a brief introduction to the parametrized Adams spectral sequence, the main technical tool used to disprove it. An example supporting the new conjectures is described.

Let k be an algebraically closed field of characteristic zero. Let c : SH → SH(k) be the functor induced by sending a space to the constant presheaf of spaces on Sm/k. We show that c is fully faithful. In particular, c induces an isomorphism c∗ : πn(E)→ Πn,0(c(E)) for all spectra E. Fix an embedding σ : k → C and let ReB : SH(k)→ SH be the associated Betti realization. Let Sk be the motivic sph...

Abstract Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, second and third author on isomorphism between Adams spectral sequence for $C\tau $ C τ algebraic Novikov $BP_{*}$ B P ∗ , we com...