# Contents

## 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 $\mathbb{A}^n$ in algebraic geometry.

Every complex analytic manifold is locally isomorphic to a polydisk.

Those analytic spaces which are subspaces of polydiscs are called affinoids.

## References

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

Revised on November 5, 2013 23:15:00 by Urs Schreiber (82.169.114.243)