On the finiteness of mod {$p$} Galois representations of a local field
Harada, Shinya
Tohoku Math. J. (2), Tome 59 (2007) no. 1, p. 67-77 / Harvested from Project Euclid
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Let $K$ be a local field and $k$ an algebraically closed field. We prove the finiteness of isomorphism classes of semisimple Galois representations of $K$ into $\GL_d(k)$ with bounded Artin conductor and residue degree. We calculate explicitly the number of totally ramified finite abelian extensions of $K$ with bounded conductor. Using this result, we give an upper bound for the number of certain Galois extensions of $K$.
Publié le : 2007-05-14
Classification:  Galois representations,  local fields,  11F80,  11S15 
@article{1176734748,
     author = {Harada, Shinya},
     title = {On the finiteness of mod {$p$} Galois representations of a local field},
     journal = {Tohoku Math. J. (2)},
     volume = {59},
     number = {1},
     year = {2007},
     pages = { 67-77},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176734748}
}

Harada, Shinya. On the finiteness of mod {$p$} Galois representations of a local field. Tohoku Math. J. (2), Tome 59 (2007) no. 1, pp.  67-77. http://gdmltest.u-ga.fr/item/1176734748/