Questions tagged [p-adic-numbers]
The p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems
253 questions
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The character of a separable degree-$p$ extension of a local field of residual characteristic $p$ ?
Let $p$ be a prime number and $F$ a finite extension of ${\mathbf Q}_p$ or of ${\mathbf F}_p((t))$. I'm going to define a natural map from the set ${\mathcal S}_p(F)$ of degree-$p$ separable ...
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On $p$-adic arithmetic softwares
I would like to automate a huge amount of computation that involves basic arithmetic operations with $p$-adic numbers. I have found a Mathematica package for it, but it is old and acts quite ...
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p-adic noninvariance of dimension
Let $p$ be a prime number. Let $n,m \geq 1$ be such that the topological spaces $\mathbb{Q}_p^n$ and $\mathbb{Q}_p^m$ are homeomorphic. Can we conclude $n=m$?
For $\mathbb{Z}_p$ it's false: In fact, ...
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