Counting real Galois covers of the projective line
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | CADORET, Anna | |
dc.date.accessioned | 2024-04-04T02:42:28Z | |
dc.date.available | 2024-04-04T02:42:28Z | |
dc.date.issued | 2005 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191245 | |
dc.description.abstractEn | We consider the following problem about Galois covers of P1 . Fixing their type of ramification that is, essentially, their monodromy group G and their branch locus, assumed to be defined over R, the question is how many covers are defined over R and how many are not? J.-P. Serre showed the number of all Galois covers with given ramification type can be computed from the character table of G. We re-use Serre's method of calculation in the more refined situation of Galois covers defined over R, for which there is a group-theoretic characterization due to P. D`ebes and M. Fried. We obtain explicit answers to our problem. As an application, we exhibit new families of covers not defined over their field of moduli and the monodromy group of which can be chosen arbitrarily large. We also give examples of Galois covers defined over the field Qtr of totally real algebraic numbers with Q-rational branch locus. | |
dc.language.iso | en | |
dc.title.en | Counting real Galois covers of the projective line | |
dc.type | Article de revue | |
bordeaux.journal | Pacific Journal of Mathematics | |
bordeaux.page | 101-129 | |
bordeaux.volume | 219 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.issue | 1 | |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-00355680 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-00355680v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Pacific%20Journal%20of%20Mathematics&rft.date=2005&rft.volume=219&rft.issue=1&rft.spage=101-129&rft.epage=101-129&rft.au=CADORET,%20Anna&rft.genre=article |
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