nLab Non-Archimedean Analysis

This page collects material related to the textbook

• Siegfried Bosch, Ulrich Güntzer, Reinhold Remmert,

  Non-Archimedean Analysis – A systematic approach to rigid analytic geometry,

  Grundlehren der Mathem. Wissen. 261, 1984

  (MR0746961, pdf)

on rigid analytic geometry.

Part A. Linear Uktrametric Analysis and Valuation Theory

Chapter 1. Norms and valuations

1.1 Semi-normed and normed groups

• normed group, triangle inequality

1.2 Semi-normed and normed rings

• normed ring

1.4 Strictly convergent power series

1.5 Non-archimedean valuations

• valuation, absolute value

Part B. Affinoid algebras

• affinoid algebra

Chapter 3. Extensions of norms and valuations

3.7 Banach algebras

Chapter 5. Strictly convergent power series

Chapter 6. Affinoid algebras and Finiteness theorems

• affinoid algebra

Part C. Rigid analytic geometry

• rigid analytic geometry

Chapter 9. Rigid analytic varieties

9.1. Grothendieck topologies

• G-topology

9.7. An application to elliptic curves

• elliptic curve

• Tate curve

category: reference