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)

  ISBN:9783540125464

  pdf

  MR0746961

on rigid analytic geometry.

Part A. Linear Ultrametric 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