# Motivic Mahowald invariants over general base fields

## TL;DR

This paper extends the concept of motivic Mahowald invariants to arbitrary fields of characteristic not two, using them to analyze periodicity in motivic stable stems and constructing lifts of classical $v_1$-periodic families.

## Contribution

It generalizes the motivic Mahowald invariant to all fields of characteristic not two and applies it to study periodicity and lift classical families in motivic stable stems.

## Key findings

- Constructed lifts of Adams' $v_1$-periodic families.
- Identified motivic Mahowald invariants of specific elements.
- Extended invariants to general base fields.

## Abstract

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 motivic Mahowald invariant over any field $F$ of characteristic not two and use it to study periodicity in the $F$-motivic stable stems. In particular, we construct lifts of some of Adams' classical $v_1$-periodic families \cite{Ada66} and identify them as the motivic Mahowald invariants of powers of $2+\rho \eta$.