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Tate Algebras

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2105)

Abstract

The Tate algebra over a complete non-Archimedean field K, say in a set of n variables, consists of all formal power series whose coefficients form a zero sequence in K. In the present chapter we develop Weierstraß Theory and use it to prove basic properties of Tate algebras.

Keywords

  • Polynomial Ring
  • Valuation Ring
  • Monic Polynomial
  • Residue Field
  • Trivial Reason

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Notes

  1. 1.

    Later, in 3.1/20, we will see that homomorphisms of Tate algebras are automatically continuous.

References

  1. S. Bosch, Algebraic Geometry and Commutative Algebra. Universitext (Springer, London, 2013)

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© 2014 Springer International Publishing Switzerland

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Bosch, S. (2014). Tate Algebras. In: Lectures on Formal and Rigid Geometry. Lecture Notes in Mathematics, vol 2105. Springer, Cham. https://doi.org/10.1007/978-3-319-04417-0_2

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