Questions tagged [kummer-theory]

The tag has no usage guidance.

6 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
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 $p \nmid n$, $m$. ...
Dimitri Koshelev's user avatar
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 ...
Ehsan Shahoseini's user avatar
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 ...
Martin Skilleter's user avatar
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 ...
JWM's user avatar
  • 183
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 ...
mmm 's user avatar
  • 1,299
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 ...
kum90's user avatar
  • 19