Abstract We prove the convergence of Adams spectral sequence based on Morava K -theory and relate it to filtration by powers maximal ideal in Lubin–Tate ring through a Miller square. use construct relating homology -local sphere derived functors completion express latter as cohomology stabiliser group. As an application, we compute zeroth limit at all primes heights.

We examine some of the basic properties satisfied by Bloch’s cycle complexes for quasi-projective varieties over a field, and extend some of them to the cycle complex of a scheme of finite type over a regular dimension one base. We also give an extension to the simplicial spectra in the niveau tower of the cosimplicial scheme ∆∗ X . As applications, we show that the AtiyahHirzebruch spectral se...

In [KWa, KWb] the need for the Brown-Peterson cohomology (for p = 2) of a product of two real projective spaces arose. In particular, they needed to understand the elements not in the tensor product and how they behaved under maps. Although quick computations with the Adams spectral sequence or the AtiyahHirzebruch spectral sequence suggest the answer, there seemed to be nothing explicit enough...

The aim of this paper is to gain explicit information about the multiplicative structure of l∗l, where l is the connective Adams summand. Our approach differs from Kane’s or Lellmann’s because our main technical tool is the MU -based Künneth spectral sequence. We prove that the algebra structure on l∗l is inherited from the multiplication on a Koszul resolution of l∗BP . Introduction Our goal i...

We provide a new and conceptually simplified construction of continuous homotopy fixed point spectra for Lubin-Tate spectra under the action of the extended Morava stabilizer group. Moreover, our new construction of a homotopy fixed point spectral sequence converging to the homotopy groups of the homotopy fixed points of Lubin-Tate spectra is isomorphic to an Adams spectral sequence converging ...

1 Katz's ring of divided congruences N. Katz [5] introduced a p-adic ring of divided congruences amongst modular forms which is closely related to the topological object KU 0 E. This ring is used to determine E * E in [1] and also proves useful in [2] for calculating the E 2-term of the Adams spectral sequence

In this paper we calculate certain functional differentials in the Adams spectral sequence converging to Wu cobordism whose values may be thought of as Hopf invariants. These results are applied to reobtain Browder's characterization: if q + 1 = 2*, there is a 2q dimensional manifold of Kervaire invariant one if and only if hi survives to EX(S°). Introduction. In 1969 Browder [2] showed that th...

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.

We show that the class of p-complete connective spectra with finitely presented cohomology over the Steenrod algebra admits a duality theory related to Brown-Comenetz duality. This construction also produces a full-plane version of the classical Adams spectral sequence for such spectra, which converges to the homotopy groups of a “finite” localization.