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Smooth curves having a large automorphism $p$-group in characteristic $p>0$.

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMATIGNON, Michel
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorROCHER, Magali
dc.date.accessioned2024-04-04T03:00:42Z
dc.date.available2024-04-04T03:00:42Z
dc.date.created2008-01-24
dc.date.issued2008
dc.identifier.issn1937-0652
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192840
dc.description.abstractEnLet $k$ be an algebraically closed field of characteristic $p>0$ and $C$ a connected nonsingular projective curve over $k$ with genus $g \geq 2$. This paper continues the work begun by Lehr and Matignon, namely the study of "big actions", i.e. the pairs $(C,G)$ where $G$ is a $p$-subgroup of the $k$-automorphism group of $C$ such that$\frac{|G|}{g} >\frac{2\,p}{p-1}$. If $G_2$ denotes the second ramification group of $G$ at the unique ramification point of the cover $C \rightarrow C/G$, we display necessary conditions on $G_2$ for $(C,G)$ to be a big action, which allows us to pursue the classification of big actions. Our main source of examples comes from the construction of curves with many rational points using ray class field theory for global function fields, as initiated by J-P. Serre and followed by Lauter and Auer. In particular, we obtain explicit examples of big actions with $G_2$ abelian of large exponent.
dc.language.isoen
dc.publisherMathematical Sciences Publishers
dc.title.enSmooth curves having a large automorphism $p$-group in characteristic $p>0$.
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.subject.halMathématiques [math]/Géométrie algébrique [math.AG]
dc.identifier.arxiv0801.1942
bordeaux.journalAlgebra & Number Theory
bordeaux.page887-926
bordeaux.volume2
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue8
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00204107
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00204107v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Algebra%20&%20Number%20Theory&rft.date=2008&rft.volume=2&rft.issue=8&rft.spage=887-926&rft.epage=887-926&rft.eissn=1937-0652&rft.issn=1937-0652&rft.au=MATIGNON,%20Michel&ROCHER,%20Magali&rft.genre=article


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