arXiv subjects

Hirofumi Nakai

Publications and source records attributed to Hirofumi Nakai.

2 recordsLinked to original sources

arXiv2018

The Method of Infinite Descent in Stable Homotopy Theory II

This paper is a continuation of the version I of the same title, which intends to clarify and expand the results in the last chapter of `the green book' by the second author. In particular, we give the stable homotopy groups of $p$-local spectra $T(m)_{(1)}$ for $m>0$. This is a part of a program to compute the $p$-components of $π_{*}(S^{0})$ through dimension $2p^{4}(p-1)$ for $p>2$. We will refer to the results from the version I freely as if they were in the first four sections of this paper, which begins with section 5.

math.AT↗

arXiv2009

On the homotopy groups of E(n)-local spectra with unusual invariant ideals

Let E(n) and T(m) for nonnegative integers n and m denote the Johnson-Wilson and the Ravenel spectra, respectively. Given a spectrum whose E(n)_*-homology is E(n)_*(T(m))/(v_1,...,v_{n-1}), then each homotopy group of it estimates the order of each homotopy group of L_nT(m). We here study the E(n)-based Adams E_2-term of it and present that the determination of the E_2-term is unexpectedly complex for odd prime case. At the prime two, we determine the E_{infty}-term for pi_*(L_2T(1)/(v_1)), whose computation is easier than that of pi_*(L_2T(1)) as we expect.

math.AT↗