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The motivic Mahowald invariant was introduced in \cite{Qui19a} and\cite{Qui19b} to study periodicity in the $\mathbb{C}$- and$\mathbb{R}$-motivic stable stems. In this paper, we define the motivicMahowald invariant over any field $F$ of characteristic not two and use it tostudy periodicity in the $F$-motivic stable stems. In particular, we constructlifts of some of Adams' classical $v_1$-periodic families \cite{Ada66} andidentify them as the motivic Mahowald invariants of powers of $2+\rho \eta$.

Motivic Mahowald invariants over general base fields