nLab
polydisc

Idea

In the context of analytic geometry, a polydisc is a product of discs: the analytic space which is formally dual to the Tate algebra? $T_n$ (for an $n$-dimensional polydisk).

This is a basic analytic space. It is the analog in analytic geometry of the affine space ${𝔸}^n$ in algebraic geometry.

Every complex analytic manifold is locally isomorphic to a polydisk.

References

• Leonard Lipshitz, Zachary Robinson, Rings of separated power series (pdf)