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Tagged with function-fields algebraic-curves
7 questions
2
votes
0
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108
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Weierstrass points in Artin-Schreier extensions of the rational function field in characteristic $p$
I encountered a problem when proving a result regarding the orders at non-Weierstrass points ($n$ is an order of the point $P$ if there is some holomorphic differential $\omega$ with order $n$ at $P$) ...
- 153
1
vote
1
answer
373
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An automorphism of a function field
I am looking for an explicit example of a function field other than rational with an automorphism which fixes places of different degrees. Also, is there a counterexample, namely a function field with ...
- 11
1
vote
1
answer
125
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Under what conditions is the compositum of two rational cubic Kummer extensions a rational function field?
Let $k$ be an algebraically closed field of characteristic $p > 3$ and $F = k(x)$ be the rational function field in the variable $x$. Consider two Kummer extensions $F_1 = F(\sqrt[3]{g_1})$, $F_2 = ...
- 38k
1
vote
1
answer
85
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Function field Towers of larger depth of recursion
A function field tower is a sequence of function fields
$$\mathcal{F}_0 \subset \mathcal{F}_1 \subset \mathcal{F}_2 \dots \subset \mathcal{F}_{n} \subset \mathcal{F}_{n+1} \subset \dots $$
over a base ...
- 6,397
2
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0
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160
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Automorphisms of function fields under constant reduction
Let $K=\mathbb{Q}(x,y)$ be a function field of genus at least 2, with defining equation $f(x,y)=0$ (say, absolutely irreducible and with coefficients not divisible by $p$), and let $k$ be the mod-$p$ ...
9
votes
2
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850
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What is the advantage of the approach of valuations to the Riemann-Roch Theorem for curves (a la Chevalley)? AKA theory of algebraic functions in one variable
Hello,
Some books and courses take the approach to Riemann-Roch for curves considering only the algebraic viewpoint of algebraic extensions of a field k(t) without going into any algebraic geometry (...
- 12.6k
2
votes
1
answer
271
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behavior of places of a function field under automorphism
if $P_{1}$ and $P_{2}$ are distinct places of equal degree of the function field F/K, and $\sigma$ is a K-field automorphism, such that $\sigma(P_{1})=P_{2}$. then, does $\deg (P_{1}\cap K(x))=\deg (...
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