Questions tagged [kummer-theory]
The kummer-theory tag has no usage guidance.
6
questions with no upvoted or accepted answers
4
votes
0
answers
80
views
The cyclic analogue of the gonality of the superelliptic curve $s^n = t^m + 1$
For naturals $n$, $m > 1$ consider the superelliptic curve $C\!: s^n = t^m + 1$, for simplicity, over an algebraically closed field of zero characteristic or large characteristic $p \nmid n$, $m$. ...
4
votes
0
answers
293
views
Reference request for Kummer-Artin-Schreier-Witt theory
I cannot find the following 4 papers by Sekiguchi–Suwa in their works on Kummer–Artin–Schreier–Witt theory:
On the unified Kummer–Artin–Schreier–Witt theory, Prépublications du laboratoire de ...
3
votes
0
answers
154
views
Lifting isogeny over étale cover
I am in the situation where I need to lift a particular isogeny over an étale cover, and I am not sure how to justify the existence of such a lift. I am trying to fill in the details of the proof of ...
2
votes
0
answers
95
views
Coboundary in Kummer theory
Let $K$ be a non archimedean local field whose residue field is of characteristic $p$. Denote by $G$ the absolute Galois group of $K$. Denote by $\mu_p$ the group of $p$-roots of unity and assume it ...
2
votes
0
answers
404
views
a reference for Kummer theory, with proofs ?
What is a standard reference for Kummer theory of semi-Abelian varieties ?
I need a complete exposition with detailed proofs. Also in prime characteristic,
although I am not sure what the statement ...
1
vote
0
answers
166
views
Is there a Kummer theory for cyclic covers in higher dimension?
Let $d \geq 2$ be an integer and $K$ a field of characteristic zero containing the roots of unity of order $d$. Let $X$ be a smooth curve over $K$, not necessarily projective. Let $\overline{x}$ be a ...