All Questions
Tagged with function-fields algebraic-number-theory
7 questions with no upvoted or accepted answers
5
votes
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answers
185
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Finite coefficients Langlands for function fields
Do we have a finite coefficients Langlands correspondence for function fields? By which I mean a bijection between Galois representations $$\pi_1(X)\to \mathrm{GL}_n\left(\overline{\mathbb{F}_p}\right)...
- 4,408
4
votes
0
answers
464
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Reference request: ramified and local geometric class field theory
There are lots of references on global unramified geometric class field theory (following Deligne's $\ell$-adic sheaves approach). There are also some notes talking about how to extend Deligne's ...
- 647
2
votes
0
answers
56
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Degeneracy maps of Drinfeld modular curves
Over number fields, we have two natural degeneracy maps
$$X_0(N)\leftarrow X_0(pN) \rightarrow X_0(N)$$
between the (compactified) moduli space of elliptic curves with level $pN$ and $N$ respectively (...
- 4,408
2
votes
0
answers
169
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Monogenic function fields
Recall that a number field $K$ is said to be monogenic if its ring of integers is of the form $\mathbb{Z}[\alpha]$, or equivalently, if it has a power integral basis. There are many references one can ...
- 103
2
votes
0
answers
109
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Weierstrass points in Artin-Schreier extensions of the rational function field in characteristic $p$
I encountered a problem when proving a result regarding the orders at non-Weierstrass points ($n$ is an order of the point $P$ if there is some holomorphic differential $\omega$ with order $n$ at $P$) ...
- 153
2
votes
0
answers
169
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A version of weak approximation with S-integers
Let $k$ be a finite field. Let $K$ a finite extension of $k(t)$. Let $S$ be a finite set of places of $K$. Let
$$K_S = \prod_{v\in S} K_v$$
where $K_v$ is the completion of $K$ at $v$. For $v\in S$, ...
- 323
2
votes
0
answers
230
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Genus of $k(T)$ is $0$ without using Riemann-Roch
Let $F$ be a function field with one variable with total constant field $k$, and let $X$ be the set of all places of $F$. How do I show that the genus of $k(T)$ is $0$ without using Riemann-Roch? Is ...
- 29