Lecture

Norms and Valuations on Fields

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In course

MATH-494: Topics in arithmetic geometry

P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Ze ...

Description

This lecture covers the construction of Qp, norms and valuations on fields, including the p-adic norm on rational numbers. It also discusses Ostrovski's theorem and the equivalence of non-trivial norms on fields. The lecture explores the properties of norms and valuations, such as the trivial norm and the torinal norm, and their significance in defining a metric space.

Official source

Ontological neighbourhood

Mathematics

Algebra: Abstract algebra

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