| Autor: |
Lorenzo, Elisa, Meleleo, Giulio, Milione, Piermarco, Bucur, Alina |
| Rok vydání: |
2015 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We study the distribution of the traces of the Frobenius endomorphism of genus $g$ curves which are quartic non-cyclic covers of $\mathbb{P}^{1}_{\mathbb{F}_{q}}$, as the curve varies in an irreducible component of the moduli space. We show that for $q$ fixed, the limiting distribution of the trace of Frobenius equals the sum of $q + 1$ independent random discrete variables. We also show that when both $g$ and $q$ go to infinity, the normalized trace has a standard complex Gaussian distribution. Finally, we extend these computations to the general case of arbitrary covers of $\mathbb{P}^{1}_{\mathbb{F}_{q}}$ with Galois group isomorphic to $r$ copies of $\mathbb{Z}/2\mathbb{Z}$. For $r = 1$, we recover the already known hyperelliptic case. We also include an appendix by Alina Bucur giving the heuristic of these distributions. |
| Databáze: |
arXiv |
| Externí odkaz: |
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