The cohomology of the Steenrod algebra and the mod $p$ Lannes-Zarati homomorphism

Abstract

In this paper, we compute ${\rm Ext}_{A}^{s}(\widetilde{H}^*(B\mathbb{Z}/p),\mathbb{F}_p)$ for $s\leq 1$. Using this result, we investigate the behavior of $\varphi_3^{\mathbb{F}_p}$ and $\varphi_s^{\widetilde{H}^*(B\mathbb{Z}/p)}\ (s\leq1)$ for an odd prime $p$.