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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- 1.
Later, in 3.1/20, we will see that homomorphisms of Tate algebras are automatically continuous.
References
S. Bosch, Algebraic Geometry and Commutative Algebra. Universitext (Springer, London, 2013)
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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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DOI: https://doi.org/10.1007/978-3-319-04417-0_2
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Print ISBN: 978-3-319-04416-3
Online ISBN: 978-3-319-04417-0
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