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Local systems which do not come from abelian varieties
[Systèmes locaux ne provenant pas de variétés abéliennes]
Paul Brommer-Wierig1 ; Yeuk Hay Joshua Lam1
1 Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin, Germany
Journal de l’École polytechnique — Mathématiques, Tome 12 (2025), pp. 341-350.

Pour chaque courbe lisse sur un corps fini nous construisons, après l’avoir privée d’un nombre fini de points, des systèmes locaux d’origine géométrique qui ne proviennent pas d’une famille de variétés abéliennes. Pour cela, nous prouvons un critère qui doit être satisfait par les systèmes locaux qui proviennent de variétés abéliennes, inspiré par un critère analogue de la théorie de Hodge en caractéristique nulle.

For each smooth curve over a finite field, after puncturing it at finitely many points, we construct local systems on it of geometric origin which do not come from a family of abelian varieties. We do so by proving a criterion which must be satisfied by local systems which do come from abelian varieties, inspired by an analogous Hodge theoretic criterion in characteristic zero.

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Accepté le :
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DOI : 10.5802/jep.292
Classification : 14F35
Keywords: Local systems, abelian varieties, Frobenius slopes
Mots-clés : Systèmes locaux, variétés abéliennes, pentes de Frobenius

Paul Brommer-Wierig 1 ; Yeuk Hay Joshua Lam 1

1 Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Paul Brommer-Wierig; Yeuk Hay Joshua Lam. Local systems which do not come from abelian varieties. Journal de l’École polytechnique — Mathématiques, Tome 12 (2025), pp. 341-350. doi : 10.5802/jep.292. https://jep.centre-mersenne.org/articles/10.5802/jep.292/

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