Timeline for Rational power series and extensions
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2017 at 9:48 | comment | added | Stefan Witzel | Here are two ways to connect the question to more "classical" maths: 1. Replace $F(x)$ by a number field (e.g. $\mathbb{Q}$) and $K$ by a non-Archimedean completion (e.g. $\mathbb{Q}_p$). In that case I don't quite know how to make sense of ``coefficients'' if the degree of $K$ is not $1$. 2. Take $F = \mathbb{C}$. Then the question is about Taylor series of meromorphic functions on Riemann surfaces. | |
| Nov 21, 2017 at 7:47 | comment | added | Stefan Witzel | 1. Another variant of the question would be: what is a characterization of power series in $F((x))$ that are algebraic over $F(x)$? 2. I am implicitly assuming that $\nu$ has degree $1$ over $F(x)$. I am also interested in the answer for valuations of higher degree even over $F(x)$. | |
| Nov 20, 2017 at 8:26 | history | asked | Stefan Witzel | CC BY-SA 3.0 |