Teichmuller lift properties
= Teichmuller lift properties
{c}
{title2=$[a]\bmod\mathfrak m_K=a,\quad[a]^q=[a]$}
For residue field $\mathbb F_q$, these two properties characterize the <Teichmuller lift> on every residue class, including zero. The <Hensel lemma> applies to $T^q-T$, whose derivative reduces to $-1$. Uniqueness implies $[ab]=[a][b]$, $[0]=0$, $[1]=1$, and $[a^p]=[a]^p$. In mixed characteristic this multiplicative section need not be additive.