Tate algebra

In rigid analysis, a branch of mathematics, the Tate algebra over a complete ultrametric field k, named for John Tate, is the subring R of the formal power series ring k[[t_1, ..., t_n]] consisting of \sum a_I t^I such that |a_I| \to 0 as I \to \infty. The maximal spectrum of R is then a rigid-analytic space.

Define the Gauss norm of f = \sum a_I t^I in R by

\|f\| = \max_I |a_I|

This makes R a Banach k-algebra.

References



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