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Nilpotence phenomena over $\mathbb{E}_{\infty}$-rings in positive characteristic
We study the behavior of nilpotent classes in $\mathbb{E}_\infty$-rings over finite fields. In characteristic $p=2$, we show that any nilpotent class can be killed by a nilpotence detecting map of $\mathbb{E}_\infty$-rings. As a consequence, we prove the existence of ``residue fields'', namely that
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