Fundamental groups and good reduction criteria for curves over positive characteristic local fields
Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 755-798.

Dans cette article je défine et étudie le groupe fondamental rigide surconvergent d’une variété algébrique sur un corps local d’équicaractéristique. C’est un (ϕ,)-module non-abélien sur l’anneu de Robba borné K , qui donne le groupe fondamental rigide classique après un changement de base vers l’anneau d’Amice K . Puis je prouve un ananlogue p-adique d’un théorème d’Oda qui dit qu’une courbe semistable sur un corps p-adique a bonne réduction si et seulement si l’action de Galois sur le groupe fondamental rendu unipotent est non-ramifiée.

In this article I define and study the overconvergent rigid fundamental group of a variety over an equicharacteristic local field. This is a non-abelian (ϕ,)-module over the bounded Robba ring K , whose underlying unipotent group (after base changing to the Amice ring K ) is exactly the classical rigid fundamental group. I then use this to prove an equicharacteristic, p-adic analogue of Oda’s theorem that a semistable curve over a p-adic field has good reduction if and only if the Galois action on its -adic unipotent fundamental group is unramified.

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DOI : https://doi.org/10.5802/jtnb.1000
Classification : 11G20,  14F35,  14F30
Mots clés : unipotent fundamental groups, function fields, monodromy, p-adic cohomology, good reduction
@article{JTNB_2017__29_3_755_0,
     author = {Christopher Lazda},
     title = {Fundamental groups and good reduction criteria for curves over positive characteristic local fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {755--798},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {29},
     number = {3},
     year = {2017},
     doi = {10.5802/jtnb.1000},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1000/}
}
Christopher Lazda. Fundamental groups and good reduction criteria for curves over positive characteristic local fields. Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 755-798. doi : 10.5802/jtnb.1000. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1000/

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