ScalingStacks

Definition 2.40. A $k$-Banach algebra $\mathcal{A}$ is called an affinoid algebra if there exists an admissible surjective homomorphism from some Tate algebra $k\{\boldsymbol{r}^{-1}\boldsymbol{T}\}$ to $\mathcal{A}$. The Banach algebra norm on an affinoid algebra $\mathcal{A}$ is called an affinoid algebra norm. If one can take $\boldsymbol{r}$ with $r_{i}=1$ for all $i\in\{1,\dots,n\}$, then $\mathcal{A}$ is called a strict affinoid algebra. One may define affinoid algebra similarly over other complete ultrametric valued field.