# Tagged Questions

In mathematics the $p$-adic number system for any prime number $p$ extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number systems.

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### Maps between spectral sequences

I am trying to understand a subtle point about how Theorem 2.2.5 is used in Kedlaya, Abbott, and Roe's "Bounding Picard numbers of surfaces using p-adic cohomology". Below I've tried to pose the ...
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### Determinant 1 matrix does not change p-adic measures

Let $f:\mathbb Z^d \rightarrow \mathbb Z^d$ be a linear map having determinant 1. Is there an obvious way to see that if $U\subseteq \mathbb Z_p^d$ is a measurable set, then the p-adic measure of $U$ ...
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### Classical geometry vs. p-adic geometry

I am interested in learning more about $p$-adic analysis and some of the geometric theories that are commonly used. However, it seems that many of the tools there are developed from analogous "...
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### Iwasawa module: $O[[G]]$ is noetherian where $G$ is a compact $p$ adic Lie group

Let $G$ be a compact $p$ adic Lie group. Let $E$ be a finite extension of $\Bbb{Q}_p$ with ring of integers $O$. Then how to show that $O[[G]]$ is noetherian. I was reading the article here and on ...
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### Spectrum theorem for p-adic matrix analysis

Recently, I met a problem related to p-adic matrices in my research, the key of the problem can be summarized in the following way: 1: whether there exist spectrum theorem for p-adic matrix.\ 2: ...
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### Proving that $\mathbb{Q}_p$ is not formally real.

I've been looking for a concrete proof without results. The only hint that I have found says: 1) $\mathbb{Q}_2$ contains a square root of $-7$. 2) $\mathbb{Q}_p$ ($p>2$) contains a square root of ...
Let $f \in \mathbb{Z}_p[x]$ and suppose $|f(a)|_p < |f'(a)|_p^2$ for some $a \in \mathbb{Z}_p$. Let $a_1 = a$, and for $n \ge 1$ let$$a_{n+1} = a_n - f(a_n)/f'(a_n).$$How do I see that this defines ...