p-adic Numbers

The report for my honours project.


For each prime p, the p-adic numbers Qp are a distinct completion of the rational numbers. We justify the significance of the p-adic absolute value, and use it to construct the p-adic numbers. We look at some of their properties, and examine the behaviour of power series over the p-adic numbers. We also construct the smallest algebraically closed complete space containing Qp.

p-adic Numbers Report

Presentation Slides