 Points on the polydisc are defined to be maximal ideals in the Tate algebra, and if "k" is algebraically closed, these correspond to points in formula_2 whose coordinates have norm at most one.An affinoid algebra is a "k"-Banach algebra that is isomorphic to a quotient of the Tate algebra by an ideal.An affinoid is then a subset of the unit polydisc on which the elements of this ideal vanish, i.e., it is the set of maximal ideals containing the ideal in question.