All Questions

Given a field $K$, one can enrich it via a valuation, an automorphism or both structures at the same time in a compatible way. In all of these three cases, the model theory is well-understood (under ...

Let $K$ be a field. Are there books or articles discussing completions of $K(x)$ with respect to the metric induced by the $p$-adic valuation $|\;\;|_p$ where $p\in k[x]$ is irreducible and different ...

Let $F$ be a field, let $F(x)$ the field of rational functions, and let $F((x))$ the field of Laurent series (which contains $F(x)$). One may ask: which series $\sum_i a_i x^i$ lie in $F(x)$? The ...

My question came when I was reading the famous Tate's paper on $p$-divisible groups. At the beginning of chapter $(2.4)$ he cites this fact as obvious. If you take a complete discrete valuation ring $...